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Journal articles on the topic 'Second order Hamiltonian systems'

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Published: 14 March 2023

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1

Schechter, Martin. "Nonautonomous second order Hamiltonian systems." Pacific Journal of Mathematics 251, no. 2 (June 3, 2011): 431–52. http://dx.doi.org/10.2140/pjm.2011.251.431.

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2

Pipan, John, and Martin Schechter. "Non-autonomous second order Hamiltonian systems." Journal of Differential Equations 257, no. 2 (July 2014): 351–73. http://dx.doi.org/10.1016/j.jde.2014.03.016.

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3

Schechter, Martin. "Periodic second order superlinear Hamiltonian systems." Journal of Mathematical Analysis and Applications 426, no. 1 (June 2015): 546–62. http://dx.doi.org/10.1016/j.jmaa.2015.01.051.

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4

Hirano, Norimichi, and Zhi-Qiang Wang. "Subharmonic solutions for second order Hamiltonian systems." Discrete & Continuous Dynamical Systems - A 4, no. 3 (1998): 467–74. http://dx.doi.org/10.3934/dcds.1998.4.467.

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5

Bonanno, Gabriele, Roberto Livrea, and Martin Schechter. "Multiple solutions of second order Hamiltonian systems." Electronic Journal of Qualitative Theory of Differential Equations, no. 33 (2017): 1–15. http://dx.doi.org/10.14232/ejqtde.2017.1.33.

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6

Llibre, Jaume, and Amar Makhlouf. "Periodic solutions of second order Hamiltonian systems." Dynamical Systems 28, no. 2 (June 2013): 214–21. http://dx.doi.org/10.1080/14689367.2013.781133.

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7

Li, Lin, and Martin Schechter. "Existence solutions for second order Hamiltonian systems." Nonlinear Analysis: Real World Applications 27 (February 2016): 283–96. http://dx.doi.org/10.1016/j.nonrwa.2015.08.001.

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8

Zhang, Qiongfen, and X. H. Tang. "Periodic solutions for second order Hamiltonian systems." Applications of Mathematics 57, no. 4 (August 2012): 407–25. http://dx.doi.org/10.1007/s10492-012-0024-9.

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9

Yang, Peixing, Jean-Pierre Françoise, and Jiang Yu. "Second Order Melnikov Functions of Piecewise Hamiltonian Systems." International Journal of Bifurcation and Chaos 30, no. 01 (January 2020): 2050016. http://dx.doi.org/10.1142/s0218127420500169.

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In this paper, we consider the general perturbations of piecewise Hamiltonian systems. A formula for the second order Melnikov functions is derived when the first order Melnikov functions vanish. As an application, we can improve an upper bound of the number of bifurcated limit cycles of a piecewise Hamiltonian system with quadratic polynomial perturbations.
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10

Zhang, Shiqing. "Periodic solutions for some second order Hamiltonian systems." Nonlinearity 22, no. 9 (July 21, 2009): 2141–50. http://dx.doi.org/10.1088/0951-7715/22/9/005.

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11

Chen, Huiwen, Zhimin He, Jianli Li, and Zigen Ouyang. "New Results for Second Order Discrete Hamiltonian Systems." Taiwanese Journal of Mathematics 21, no. 2 (March 2017): 403–28. http://dx.doi.org/10.11650/tjm/7762.

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12

Tang, X. H., and Xingyong Zhang. "Periodic solutions for second-order discrete Hamiltonian systems." Journal of Difference Equations and Applications 17, no. 10 (October 2011): 1413–30. http://dx.doi.org/10.1080/10236190903555237.

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13

Liu, Zhisu, Shangjiang Guo, and Ziheng Zhang. "Homoclinic orbits for the second-order Hamiltonian systems." Nonlinear Analysis: Real World Applications 36 (August 2017): 116–38. http://dx.doi.org/10.1016/j.nonrwa.2016.12.006.

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14

Abramov, A. A., V. I. Ul’yanova, and L. F. Yukhno. "Nonlinear eigenvalue problem for second-order Hamiltonian systems." Computational Mathematics and Mathematical Physics 48, no. 6 (June 2008): 942–45. http://dx.doi.org/10.1134/s0965542508060067.

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15

Deng, Yiyang, Fengying Li, Bingyu Li, and Ying lv. "Periodic solutions for nonsmooth second-order Hamiltonian systems." Mathematical Methods in the Applied Sciences 41, no. 18 (October 18, 2018): 9502–10. http://dx.doi.org/10.1002/mma.5308.

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16

Luan, Shi Xia, and An Min Mao. "Periodic Solutions of Nonautonomous Second Order Hamiltonian Systems." Acta Mathematica Sinica, English Series 21, no. 4 (July 1, 2005): 685–90. http://dx.doi.org/10.1007/s10114-005-0532-6.

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17

Schechter, Martin. "Homoclinic solutions of nonlinear second-order Hamiltonian systems." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 5 (November 4, 2015): 1665–83. http://dx.doi.org/10.1007/s10231-015-0538-3.

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18

Yurduşen, İsmet. "Second-Order Integrals for Systems inE2Involving Spin." Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/952646.

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In two-dimensional Euclidean plane, existence of second-order integrals of motion is investigated for integrable Hamiltonian systems involving spin (e.g., those systems describing interaction between two particles with spin 0 and spin 1/2) and it has been shown that no nontrivial second-order integrals of motion exist for such systems.
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19

Lv, Haiyan, and Guanwei Chen. "Homoclinic orbits for periodic second order Hamiltonian systems with superlinear terms." Electronic Journal of Qualitative Theory of Differential Equations, no. 61 (2022): 1–9. http://dx.doi.org/10.14232/ejqtde.2022.1.61.

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We obtain the existence of nontrivial homoclinic orbits for nonautonomous second order Hamiltonian systems by using critical point theory under some different superlinear conditions from those previously used in Hamiltonian systems. In particular, an example is given to illustrate our result.
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20

Smetanová, Dana. "Higher Order Hamiltonian Systems with Generalized Legendre Transformation." Mathematics 6, no. 9 (September 10, 2018): 163. http://dx.doi.org/10.3390/math6090163.

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The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition.
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21

Wang, Da-Bin, and Man Guo. "Multiple periodic solutions for second-order discrete Hamiltonian systems." Journal of Nonlinear Sciences and Applications 10, no. 02 (February 5, 2017): 410–18. http://dx.doi.org/10.22436/jnsa.010.02.07.

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22

Ye, Yiwei, and Chun-Lei Tang. "Multiple Homoclinic Solutions for Second-Order Perturbed Hamiltonian Systems." Studies in Applied Mathematics 132, no. 2 (June 25, 2013): 112–37. http://dx.doi.org/10.1111/sapm.12023.

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23

Jarab'ah, Ola. "Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian." American Journal of Physics and Applications 6, no. 4 (2018): 85. http://dx.doi.org/10.11648/j.ajpa.20180604.12.

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24

Long, Yi Ming. "Multiple solutions of perturbed superquadratic second order Hamiltonian systems." Transactions of the American Mathematical Society 311, no. 2 (February 1, 1989): 749. http://dx.doi.org/10.1090/s0002-9947-1989-0978375-4.

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25

An, Tianqing, and Yiming Long. "On the index theories for second order Hamiltonian systems." Nonlinear Analysis 34, no. 4 (November 1998): 585–92. http://dx.doi.org/10.1016/s0362-546x(97)00572-5.

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26

Jiang, Mei-Yue. "Periodic solutions of partially superquadratic second order Hamiltonian systems." Nonlinear Analysis: Theory, Methods & Applications 64, no. 9 (May 2006): 1946–61. http://dx.doi.org/10.1016/j.na.2005.07.031.

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27

ZHAO, XiaoXiao, ShiQing ZHANG, and FengYing LI. "Periodic solutions of non-autonomous second order Hamiltonian systems." SCIENTIA SINICA Mathematica 44, no. 12 (November 1, 2014): 1257–62. http://dx.doi.org/10.1360/012014-54.

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28

Zhang, Qingye, and Chungen Liu. "Infinitely many homoclinic solutions for second order Hamiltonian systems." Nonlinear Analysis: Theory, Methods & Applications 72, no. 2 (January 2010): 894–903. http://dx.doi.org/10.1016/j.na.2009.07.021.

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29

Celletti, A., and J. P. Francoise. "Matrix-second order differential equations and chaotic Hamiltonian systems." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 40, no. 6 (November 1989): 925–30. http://dx.doi.org/10.1007/bf00945813.

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30

Zhang, Qingye, and Chungen Liu. "Infinitely many periodic solutions for second order Hamiltonian systems." Journal of Differential Equations 251, no. 4-5 (August 2011): 816–33. http://dx.doi.org/10.1016/j.jde.2011.05.021.

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31

Ye, Yi-Wei, and Chun-Lei Tang. "Periodic solutions for some nonautonomous second order Hamiltonian systems." Journal of Mathematical Analysis and Applications 344, no. 1 (August 2008): 462–71. http://dx.doi.org/10.1016/j.jmaa.2008.03.021.

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32

Zhang, Xingyong, and Yinggao Zhou. "Periodic solutions of non-autonomous second order Hamiltonian systems." Journal of Mathematical Analysis and Applications 345, no. 2 (September 2008): 929–33. http://dx.doi.org/10.1016/j.jmaa.2008.05.026.

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33

Cordaro, Giuseppe, and Giuseppe Rao. "Three periodic solutions for perturbed second order Hamiltonian systems." Journal of Mathematical Analysis and Applications 359, no. 2 (November 2009): 780–85. http://dx.doi.org/10.1016/j.jmaa.2009.06.049.

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34

Bhatt, Ashish, Dwayne Floyd, and Brian E. Moore. "Second Order Conformal Symplectic Schemes for Damped Hamiltonian Systems." Journal of Scientific Computing 66, no. 3 (June 24, 2015): 1234–59. http://dx.doi.org/10.1007/s10915-015-0062-z.

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35

Blot, Joël. "Almost periodic solutions of forced second order hamiltonian systems." Annales de la faculté des sciences de Toulouse Mathématiques 12, no. 3 (1991): 351–63. http://dx.doi.org/10.5802/afst.730.

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36

Yan, Sheng-Hua, Xing-Ping Wu, and Chun-Lei Tang. "Multiple periodic solutions for second-order discrete Hamiltonian systems." Applied Mathematics and Computation 234 (May 2014): 142–49. http://dx.doi.org/10.1016/j.amc.2014.01.160.

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37

Tao, Zhu-Lian, and Chun-Lei Tang. "Periodic and subharmonic solutions of second-order Hamiltonian systems." Journal of Mathematical Analysis and Applications 293, no. 2 (May 2004): 435–45. http://dx.doi.org/10.1016/j.jmaa.2003.11.007.

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38

Tang, Chun-Lei, and Xing-Ping Wu. "Subharmonic solutions for nonautonomous sublinear second order Hamiltonian systems." Journal of Mathematical Analysis and Applications 304, no. 1 (April 2005): 383–93. http://dx.doi.org/10.1016/j.jmaa.2004.09.032.

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39

Yang, Rigao. "Periodic solutions of some autonomous second order Hamiltonian systems." Journal of Applied Mathematics and Computing 28, no. 1-2 (March 29, 2008): 51–58. http://dx.doi.org/10.1007/s12190-008-0075-y.

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40

Xiao, Huafeng. "A Note on the Minimal Period Problem for Second Order Hamiltonian Systems." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/385381.

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We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature.
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41

Chávez, Matías, Thomas Wiegand, Alexander A. Malär, Beat H. Meier, and Matthias Ernst. "Residual dipolar line width in magic-angle spinning proton solid-state NMR." Magnetic Resonance 2, no. 1 (July 1, 2021): 499–509. http://dx.doi.org/10.5194/mr-2-499-2021.

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Abstract. Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1/ωr dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ωr-2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.
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42

GAVRILOV, LUBOMIR, and ILIYA D. ILIEV. "Second-order analysis in polynomially perturbed reversible quadratic Hamiltonian systems." Ergodic Theory and Dynamical Systems 20, no. 6 (December 2000): 1671–86. http://dx.doi.org/10.1017/s0143385700000936.

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We study degree $n$ polynomial perturbations of quadratic reversible Hamiltonian vector fields with one center and one saddle point. It was recently proved that if the first Poincaré–Pontryagin integral is not identically zero, then the exact upper bound for the number of limit cycles on the finite plane is $n-1$. In the present paper we prove that if the first Poincaré–Pontryagin function is identically zero, but the second is not, then the exact upper bound for the number of limit cycles on the finite plane is $2(n-1)$. In the case when the perturbation is quadratic ($n=2$) we obtain a complete result—there is a neighborhood of the initial Hamiltonian vector field in the space of all quadratic vector fields, in which any vector field has at most two limit cycles.
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43

Pankov, Alexander. "Homoclinics for strongly indefinite almost periodic second order Hamiltonian systems." Advances in Nonlinear Analysis 8, no. 1 (April 19, 2017): 372–85. http://dx.doi.org/10.1515/anona-2017-0041.

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Abstract Under certain assumptions, we prove the existence of homoclinic solutions for almost periodic second order Hamiltonian systems in the strongly indefinite case. The proof relies on a careful analysis of the energy functional restricted to the generalized Nehari manifold, and the existence and fine properties of special Palais–Smale sequences.
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44

Cheng, Xu-Hui, and Guo-Qing Huang. "A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries." Symmetry 13, no. 4 (April 1, 2021): 584. http://dx.doi.org/10.3390/sym13040584.

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In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.
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45

Tabarrok, B., and C. M. Leech. "Hamiltonian Mechanics for Functionals Involving Second-Order Derivatives." Journal of Applied Mechanics 69, no. 6 (October 31, 2002): 749–54. http://dx.doi.org/10.1115/1.1505626.

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Hamilton’s principle was developed for the modeling of dynamic systems in which time is the principal independent variable and the resulting equations of motion are second-order differential equations. This principle uses kinetic energy which is functionally dependent on first-order time derivatives, and potential energy, and has been extended to include virtual work. In this paper, a variant of Hamiltonian mechanics for systems whose motion is governed by fourth-order differential equations is developed and is illustrated by an example invoking the flexural analysis of beams. The variational formulations previously associated with Newton’s second-order equations of motion have been generalized to encompass problems governed by energy functionals involving second-order derivatives. The canonical equations associated with functionals with second order derivatives emerge as four first-order equations in each variable. The transformations of these equations to a new system wherein the generalized variables and momenta appear as constants, can be obtained through several different forms of generating functions. The generating functions are obtained as solutions of the Hamilton-Jacobi equation. This theory is illustrated by application to an example from beam theory the solution recovered using a technique for solving nonseparable forms of the Hamilton-Jacobi equation. Finally whereas classical variational mechanics uses time as the primary independent variable, here the theory is extended to include static mechanics problems in which the primary independent variable is spatial.
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46

Naz, Rehana, and Imran Naeem. "The Artificial Hamiltonian, First Integrals, and Closed-Form Solutions of Dynamical Systems for Epidemics." Zeitschrift für Naturforschung A 73, no. 4 (March 28, 2018): 323–30. http://dx.doi.org/10.1515/zna-2017-0399.

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AbstractThe non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form ${\dot q^i} = \frac{{\partial H}}{{\partial {p_i}}},{\text{ }}{\dot p^i} = - \frac{{\partial H}}{{\partial {q_i}}} + {\Gamma ^i}(t,{\text{ }}{q^i},{\text{ }}{p_i})$ appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term ‘artificial Hamiltonian’ for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.
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47

Kuang, Juhong, and Weiyi Chen. "Minimal period problem for second-order Hamiltonian systems with asymptotically linear nonlinearities." Open Mathematics 20, no. 1 (January 1, 2022): 974–85. http://dx.doi.org/10.1515/math-2022-0473.

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Abstract By applying the combination of discrete variational method and approximation, developed in a previous study [J. Kuang, W. Chen, and Z. Guo, Periodic solutions with prescribed minimal period for second-order even Hamiltonian systems, Commun. Pure Appl. Anal. 21 (2022), no. 1, 47–59], we overcome some difficulties in the absence of Ambrosetti-Rabinowitz condition and obtain new sufficient conditions for the existence of periodic solutions with prescribed minimal period for second-order Hamiltonian systems with asymptotically linear nonlinearities.
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48

Wan, Li-Li, and Li-Kang Xiao. "Homoclinic solutions for a class of second order Hamiltonian systems." Differential Equations & Applications, no. 2 (2012): 257–65. http://dx.doi.org/10.7153/dea-04-15.

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49

Zelati, Vittorio Coti, and Paul H. Rabinowitz. "Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials." Journal of the American Mathematical Society 4, no. 4 (October 1991): 693. http://dx.doi.org/10.2307/2939286.

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50

HOU, Duo, Shumei ZHANG, and Juan HU. "Periodic Solution of Some Non-Autonomous Second Order Hamiltonian Systems." Acta Analysis Functionalis Applicata 14, no. 1 (2012): 71. http://dx.doi.org/10.3724/sp.j.1160.2012.00071.

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