Journal articles: 'Liouville systems'

1

Chetverikov, V. N. "Liouville systems and symmetries." Differential Equations 48, no. 12 (December 2012): 1639–51. http://dx.doi.org/10.1134/s0012266112120099.

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2

Wang, Guofang. "Moser-Trudinger inequalities and Liouville systems." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 328, no. 10 (May 1999): 895–900. http://dx.doi.org/10.1016/s0764-4442(99)80293-6.

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3

Lin, Chang-Shou. "Liouville Systems of Mean Field Equations." Milan Journal of Mathematics 79, no. 1 (June 2011): 81–94. http://dx.doi.org/10.1007/s00032-011-0149-4.

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4

Zhuo, Ran, and FengQuan Li. "Liouville type theorems for Schrödinger systems." Science China Mathematics 58, no. 1 (November 21, 2014): 179–96. http://dx.doi.org/10.1007/s11425-014-4925-9.

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5

Demskoi, D. K. "One Class of Liouville-Type Systems." Theoretical and Mathematical Physics 141, no. 2 (November 2004): 1509–27. http://dx.doi.org/10.1023/b:tamp.0000046560.84634.8c.

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6

Battaglia, Luca, Francesca Gladiali, and Massimo Grossi. "Nonradial entire solutions for Liouville systems." Journal of Differential Equations 263, no. 8 (October 2017): 5151–74. http://dx.doi.org/10.1016/j.jde.2017.06.009.

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7

Chipot, M., I. Shafrir, and G. Wolansky. "On the Solutions of Liouville Systems." Journal of Differential Equations 140, no. 1 (October 1997): 59–105. http://dx.doi.org/10.1006/jdeq.1997.3316.

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8

Chipot, M., I. Shafrir, and G. Wolansky. "On the Solutions of Liouville Systems." Journal of Differential Equations 178, no. 2 (January 2002): 630. http://dx.doi.org/10.1006/jdeq.2001.4105.

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9

Borisova, Galina. "Sturm - Liouville systems and nonselfadjoint operators, presented as couplings of dissipative and antidissipative operators with real absolutely continuous spectra." Annual of Konstantin Preslavsky University of Shumen, Faculty of mathematics and informatics XXIII C (2022): 11–21. http://dx.doi.org/10.46687/wxfc2019.

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This paper is a continuation of the considerations of the paper [1] and it presents the connection between Sturm-Liouville systems and Livšic operator colligations theory. An usefull representation of solutions of Sturm - Liouville systems is obtained using the resolvent of operators from a large class of nonselfadjoint nondissipative operators, presented as couplings of dissipative and antidissipative operators with real spectra. A connection between Sturm-Liouville systems and the inner state of the corresponding open system of operators from the considered class is presented.

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10

Rynne, Bryan P. "The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (February 1993): 35–47. http://dx.doi.org/10.1017/s0013091500005873.

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This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.

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11

Rynne, Bryan P. "The asymptotic distribution of the eigenvalues of multiparameter Sturm–Liouville systems II." Proceedings of the Edinburgh Mathematical Society 37, no. 2 (June 1994): 301–16. http://dx.doi.org/10.1017/s0013091500006088.

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In a previous paper we studied the asymptotic distribution of the multiparameter eigenvalues of uniformly right definite multiparameter Sturm–Liouville eigenvalue problems. In this paper we extend the analysis to deal with multiparameter Sturm–Liouville problems satisfying uniform left definiteness, and non-uniform left and right definiteness.

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12

Kibkalo, V., A. Fomenko, and I. Kharcheva. "Realizing integrable Hamiltonian systems by means of billiard books." Transactions of the Moscow Mathematical Society 82 (March 15, 2022): 37–64. http://dx.doi.org/10.1090/mosc/324.

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Fomenko’s conjecture that the topology of the Liouville foliations associated with integrable smooth or analytic Hamiltonian systems can be realized by means of integrable billiard systems is discussed. An algorithm of Vedyushkina and Kharcheva’s realizing 3-atoms by billiard books, which has been simplified significantly by formulating it in terms of f f -graphs, is presented. Note that, using another algorithm, Vedyushkina and Kharcheva have also realized an arbitrary type of the base of the Liouville foliation on the whole 3-dimensional isoenergy surface. This algorithm is illustrated graphically by an example where the invariant of the well-known Joukowsky system (the Euler case with a gyrostat) is realized for a certain energy range. It turns out that the entire Liouville foliation, rather than just the class of its base, is realized there; that is, the billiard and mechanical systems turn out to be Liouville equivalent. Results due to Vedyushkina and Kibkalo on constructing billiards with arbitrary values of numerical invariants are also presented. For billiard books without potential that possess a certain property, the existence of a Fomenko–Zieschang invariant is shown; it is also proved that they belong to the class of topologically stable systems. Finally, an example is presented when the addition of a Hooke potential to a planar billiard produces a splitting nondegenerate 4-singularity of rank 1.

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13

M, Nandakumar, and K. S. Subrahamanian Moosath. "Rough Liouville Equivalence of Integrable Hamiltonian Systems." Advances in Dynamical Systems and Applications 15, no. 2 (December 22, 2020): 153–69. http://dx.doi.org/10.37622/adsa/15.2.2020.153-169.

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14

Gallegos, Javier, and Manuel Duarte-Mermoud. "Asymptotic analysis of Riemann–Liouville fractional systems." Electronic Journal of Qualitative Theory of Differential Equations, no. 73 (2018): 1–16. http://dx.doi.org/10.14232/ejqtde.2018.1.73.

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15

FARINA, ALBERTO. "A LIOUVILLE PROPERTY FOR GINZBURG–LANDAU SYSTEMS." Analysis and Applications 05, no. 03 (July 2007): 285–90. http://dx.doi.org/10.1142/s0219530507000985.

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In this short paper, we consider solutions u ∈ C2(ℝN, ℝM) (with N,M ≥ 1) of the Ginzburg–Landau system Δu = u(|u|2 - 1). For N = 3 and M = 2, we prove that every solution satisfying ∫ℝ3 (|u|2 - 1)2 < +∞, is constant and of unit norm. We also give necessary and sufficient conditions, on the integers N and M, ensuring a Liouville property for finite potential energy solutions of the system under consideration.

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16

Wang, Weimin, and Li Hong. "Liouville-type theorems for semilinear elliptic systems." Nonlinear Analysis: Theory, Methods & Applications 75, no. 13 (September 2012): 5380–91. http://dx.doi.org/10.1016/j.na.2012.04.057.

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17

Qu, Changzheng, and Liu Chao. "Heterotic Liouville systems from the Bernoulli equation." Physics Letters A 199, no. 5-6 (April 1995): 349–52. http://dx.doi.org/10.1016/0375-9601(95)00147-u.

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18

Kiselev, A. V., and J. W. van de Leur. "Symmetry algebras of Lagrangian Liouville-type systems." Theoretical and Mathematical Physics 162, no. 2 (February 2010): 149–62. http://dx.doi.org/10.1007/s11232-010-0011-9.

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19

DʼAmbrosio, Lorenzo, and Enzo Mitidieri. "Liouville theorems for elliptic systems and applications." Journal of Mathematical Analysis and Applications 413, no. 1 (May 2014): 121–38. http://dx.doi.org/10.1016/j.jmaa.2013.11.052.

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20

Duviryak, A., and A. Nazarenko. "Liouville equation for the systems with constraints." Journal of Physical Studies 3, no. 4 (1999): 399–408. http://dx.doi.org/10.30970/jps.03.399.

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21

Gu, Yi, and Lei Zhang. "Degree counting theorems for singular Liouville systems." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 21, no. 2 (December 2020): 1103–35. http://dx.doi.org/10.2422/2036-2145.201812_007.

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22

Zhang, Zhengce. "Liouville-Type Theorems for Some Integral Systems." Applied Mathematics 01, no. 02 (2010): 94–100. http://dx.doi.org/10.4236/am.2010.12012.

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23

Barrett, Louis C., and Dennis N. Winslow. "Interlacing theorems for interface Sturm-Liouville systems." Journal of Mathematical Analysis and Applications 129, no. 2 (February 1988): 533–59. http://dx.doi.org/10.1016/0022-247x(88)90270-3.

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24

Battaglia, Luca. "Moser–Trudinger inequalities for singular Liouville systems." Mathematische Zeitschrift 282, no. 3-4 (November 23, 2015): 1169–90. http://dx.doi.org/10.1007/s00209-015-1584-7.

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25

Jin, Jiaming. "Existence results for Liouville equations and systems." Journal of Mathematical Analysis and Applications 491, no. 2 (November 2020): 124325. http://dx.doi.org/10.1016/j.jmaa.2020.124325.

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26

Fomenko, A. T. "Topological invariants of Liouville integrable Hamiltonian systems." Functional Analysis and Its Applications 22, no. 4 (1989): 286–96. http://dx.doi.org/10.1007/bf01077420.

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27

Cai, Guocai, Hongjing Pan, and Ruixiang Xing. "A Note on Parabolic Liouville Theorems and Blow-Up Rates for a Higher-Order Semilinear Parabolic System." International Journal of Differential Equations 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/896427.

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We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable onR. As an immediate application of the parabolic Liouville-type theorems, the range of the exponent in blow-up rates for the corresponding systems is also improved.

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28

Fu, Jing-Li, Lijun Zhang, Chaudry Khalique, and Ma-Li Guo. "Circulatory integral and Routh's equations of Lagrange systems with Riemann-Liouville fractional derivatives." Thermal Science 25, no. 2 Part B (2021): 1355–63. http://dx.doi.org/10.2298/tsci200520034f.

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In this paper, the circulatory integral and Routh?s equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, and the circulatory integral of Lagrange systems is obtained by making use of the relationship between Riemann-Liouville fractional integrals and fractional derivatives. Thereafter, the Routh?s equations of Lagrange systems are given based on the fractional circulatory integral. Two examples are presented to illustrate the application of the results.

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29

Smyrnelis, Panayotis. "Gradient estimates for semilinear elliptic systems and other related results." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 6 (October 22, 2015): 1313–30. http://dx.doi.org/10.1017/s0308210515000347.

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A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress–energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.

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30

Denton, Zachary, and Juan Diego Ramírez. "Quasilinearization method for finite systems of nonlinear RL fractional differential equations." Opuscula Mathematica 40, no. 6 (2020): 667–83. http://dx.doi.org/10.7494/opmath.2020.40.6.667.

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In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order \(0\lt q\lt 1\). Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.

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31

Neamaty, A., and S. Mosazadeh. "On the Canonical Solution of the Sturm–Liouville Problem with Singularity and Turning Point of Even Order." Canadian Mathematical Bulletin 54, no. 3 (September 1, 2011): 506–18. http://dx.doi.org/10.4153/cmb-2011-069-7.

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AbstractIn this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm–Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm–Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm–Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.

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32

Luo, Lin, and Engui Fan. "Finite-Dimensional Hamiltonian Systems from Li Spectral Problem by Symmetry Constraints." Zeitschrift für Naturforschung A 62, no. 7-8 (August 1, 2007): 399–405. http://dx.doi.org/10.1515/zna-2007-7-808.

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A hierarchy associated with the Li spectral problem is derived with the help of the zero curvature equation. It is shown that the hierarchy possesses bi-Hamiltonian structure and is integrable in the Liouville sense. Moreover, the mono- and binary-nonlinearization theory can be successfully applied in the spectral problem. Under the Bargmann symmetry constraints, Lax pairs and adjoint Lax pairs are nonlineared into finite-dimensional Hamiltonian systems (FDHS) in the Liouville sense. New involutive solutions for the Li hierarchy are obtained.

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33

TARASOV, VASILY E. "TRANSPORT EQUATIONS FROM LIOUVILLE EQUATIONS FOR FRACTIONAL SYSTEMS." International Journal of Modern Physics B 20, no. 03 (January 30, 2006): 341–53. http://dx.doi.org/10.1142/s0217979206033267.

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We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Gasdynamic equations for fractional systems are derived from the generalized transport equation.

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34

Pan, Xue, Xiuwen Li, and Jing Zhao. "Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/216919.

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We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. Then, by using generally mild conditions of cost functional, we extend the existence result of optimal controls to the Riemann-Liouville fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results.

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35

Tuan Duong, Anh, and Quoc Hung Phan. "A Liouville-type theorem for cooperative parabolic systems." Discrete & Continuous Dynamical Systems - A 38, no. 2 (2018): 823–33. http://dx.doi.org/10.3934/dcds.2018035.

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36

D'Ambrosio, Lorenzo, and Enzo Mitidieri. "Hardy-Littlewood-Sobolev systems and related Liouville theorems." Discrete & Continuous Dynamical Systems - S 7, no. 4 (2014): 653–71. http://dx.doi.org/10.3934/dcdss.2014.7.653.

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37

Liu, Jian. "Path integral Liouville dynamics for thermal equilibrium systems." Journal of Chemical Physics 140, no. 22 (June 14, 2014): 224107. http://dx.doi.org/10.1063/1.4881518.

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38

Littlejohn, Lance L., and Allan M. Krall. "Orthogonal polynomials and singular Sturm-Liouville Systems, I." Rocky Mountain Journal of Mathematics 16, no. 3 (September 1986): 435–80. http://dx.doi.org/10.1216/rmj-1986-16-3-435.

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39

Hile, G. N., and Chiping Zhou. "Liouville theorems for elliptic systems of arbitrary order." Applicable Analysis 73, no. 1-2 (October 1999): 115–30. http://dx.doi.org/10.1080/00036819908840768.

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40

LI, YUQIANG. "RIEMANN–LIOUVILLE PROCESSES ARISING FROM BRANCHING PARTICLE SYSTEMS." Stochastics and Dynamics 13, no. 03 (May 27, 2013): 1250022. http://dx.doi.org/10.1142/s0219493712500220.

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It is proved in this paper that Riemann–Liouville processes can arise from the temporal structures of the scaled occupation time fluctuation limits of the site-dependent (d, α, σ(x)) branching particle systems in the case of 1 = d < α < 2 and ∫ℝ σ(x) d x < ∞.

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41

Annaby, M. H., J. Bustoz, and M. E. H. Ismail. "On sampling theory and basic Sturm–Liouville systems." Journal of Computational and Applied Mathematics 206, no. 1 (September 2007): 73–85. http://dx.doi.org/10.1016/j.cam.2006.05.024.

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42

Gorovoy, O., and E. Ivanov. "Superfield actions for N = 4 WZNW-Liouville systems." Nuclear Physics B 381, no. 1-2 (August 1992): 394–412. http://dx.doi.org/10.1016/0550-3213(92)90653-s.

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43

Liu, Jiaqun, Yuxia Guo, and Yajing Zhang. "Liouville-type theorems for polyharmonic systems in RN." Journal of Differential Equations 225, no. 2 (June 2006): 685–709. http://dx.doi.org/10.1016/j.jde.2005.10.016.

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44

Kobayashi, Mei. "Sturm-Liouville systems with potentials 0.5 cos 2nx." Journal of Computational Physics 94, no. 2 (June 1991): 487–93. http://dx.doi.org/10.1016/0021-9991(91)90232-a.

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45

Liu, Song, Xiang Wu, Xian-Feng Zhou, and Wei Jiang. "Asymptotical stability of Riemann–Liouville fractional nonlinear systems." Nonlinear Dynamics 86, no. 1 (June 3, 2016): 65–71. http://dx.doi.org/10.1007/s11071-016-2872-4.

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46

Teramoto, Tomomitsu, and Hiroyuki Usami. "A Liouville type theorem for semilinear elliptic systems." Pacific Journal of Mathematics 204, no. 1 (May 1, 2002): 247–55. http://dx.doi.org/10.2140/pjm.2002.204.247.

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47

Vries, D., K. J. Keesman, and H. Zwart. "Luenberger boundary observer synthesis for Sturm–Liouville systems." International Journal of Control 83, no. 7 (July 2010): 1504–14. http://dx.doi.org/10.1080/00207179.2010.481768.

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48

Lange, Charles G. "Asymptotic Analysis of Forced Nonlinear Sturm-Liouville Systems." Studies in Applied Mathematics 76, no. 3 (June 1987): 239–63. http://dx.doi.org/10.1002/sapm1987763239.

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49

Liu, Song, Xiang Wu, Yan-Jie Zhang, and Ran Yang. "Asymptotical stability of Riemann–Liouville fractional neutral systems." Applied Mathematics Letters 69 (July 2017): 168–73. http://dx.doi.org/10.1016/j.aml.2017.02.016.

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50

Zhang, Yajing. "A Liouville type theorem for polyharmonic elliptic systems." Journal of Mathematical Analysis and Applications 326, no. 1 (February 2007): 677–90. http://dx.doi.org/10.1016/j.jmaa.2006.03.027.

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Journal articles on the topic 'Liouville systems'

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