Relevant bibliographies by topics / Positively homogeneous Hamiltonians

Academic literature on the topic 'Positively homogeneous Hamiltonians'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Positively homogeneous Hamiltonians"

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Fonda, Alessandro. "Positively homogeneous hamiltonian systems in the plane." Journal of Differential Equations 200, no. 1 (June 2004): 162–84. http://dx.doi.org/10.1016/j.jde.2004.02.001.

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2

Wang, Shuang, and Dingbian Qian. "Subharmonic Solutions of Indefinite Hamiltonian Systems via Rotation Numbers." Advanced Nonlinear Studies 21, no. 3 (July 17, 2021): 557–78. http://dx.doi.org/10.1515/ans-2021-2134.

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Abstract We investigate the multiplicity of subharmonic solutions for indefinite planar Hamiltonian systems J ⁢ z ′ = ∇ ⁡ H ⁢ ( t , z ) {Jz^{\prime}=\nabla H(t,z)} from a rotation number viewpoint. The class considered is such that the behaviour of its solutions near zero and infinity can be compared two suitable positively homogeneous systems. Our approach can be used to deal with the problems in absence of the sign assumption on ∂ ⁡ H ∂ ⁡ x ⁢ ( t , x , y ) {\frac{\partial H}{\partial x}(t,x,y)} , uniqueness and global continuability for the solutions of the associated Cauchy problems. These systems may also be resonant. By the use of an approach of rotation number, the phase-plane analysis of the spiral properties of large solutions and a recent version of Poincaré–Birkhoff theorem for Hamiltonian systems, we are able to extend previous multiplicity results of subharmonic solutions for asymptotically semilinear systems to indefinite planar Hamiltonian systems.
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Ruzhansky, Michael, Niyaz Tokmagambetov, and Berikbol T. Torebek. "Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations." Journal of Inverse and Ill-posed Problems 27, no. 6 (December 1, 2019): 891–911. http://dx.doi.org/10.1515/jiip-2019-0031.

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Abstract A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as well as on the fractional time diffusion (subdiffusion) equations are presented. Consequently, the obtained results are applied for the similar inverse problems for a large class of subelliptic diffusion and subdiffusion equations (with continuous spectrum). Such problems are modelled by using general homogeneous left-invariant hypoelliptic operators on general graded Lie groups. A list of examples is discussed, including Sturm–Liouville problems, differential models with involution, fractional Sturm–Liouville operators, harmonic and anharmonic oscillators, Landau Hamiltonians, fractional Laplacians, and harmonic and anharmonic operators on the Heisenberg group. The rod cooling problem for the diffusion with involution is modelled numerically, showing how to find a “cooling function”, and how the involution normally slows down the cooling speed of the rod.
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Misztela, Arkadiusz. "Reduction of lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations." ESAIM: Control, Optimisation and Calculus of Variations, July 19, 2022. http://dx.doi.org/10.1051/cocv/2022051.

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This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the optimal control theory. We present a necessary and sufficient condition for a reduction of a Hamiltonian satisfying optimality conditions to the case when the Hamiltonian is positively homogeneous and also satisfies optimality conditions. It allows us to reduce some uniqueness problems of lower semicontinuous solutions to Barron-Jensen and Frankowska theorems. For Hamiltonians, which cannot be reduced in that way, we prove the new existence and uniqueness theorems.
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Fabry, Christian, and Alessandro Fonda. "Unbounded Motions of Perturbed Isochronous Hamiltonian Systems at Resonance." Advanced Nonlinear Studies 5, no. 3 (January 1, 2005). http://dx.doi.org/10.1515/ans-2005-0303.

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AbstractLarge amplitude solutions of asymptotically positively homogeneous perturbations of hamiltonians systems at resonance can be unbounded, either in the past, or in the future. We present conditions for boundedness or unboundedness, generalizing in particular the results obtained by Alonso and Ortega [1] for scalar second order equations with asymmetric nonlinearities.
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Fonda, Alessandro, Giuliano Klun, Franco Obersnel, and Andrea Sfecci. "On the Dirichlet problem associated with bounded perturbations of positively-(p, q)- homogeneous Hamiltonian systems." Journal of Fixed Point Theory and Applications 24, no. 4 (September 21, 2022). http://dx.doi.org/10.1007/s11784-022-00980-7.

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AbstractThe existence of solutions for the Dirichlet problem associated with bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems is considered both in nonresonant and resonant situations. To deal with the resonant case, the existence of a couple of lower and upper solutions is assumed. Both the well-ordered and the non-well-ordered cases are analysed. The proof is based on phase-plane analysis and topological degree theory.
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Kaveh, Kiumars, Christopher Manon, and Takuya Murata. "On Degenerations of Projective Varieties to Complexity-One T-Varieties." International Mathematics Research Notices, April 20, 2022. http://dx.doi.org/10.1093/imrn/rnac075.

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Abstract Let $R$ be a positively graded finitely generated $\textbf {k}$-domain with Krull dimension $d+1$. We show that there is a homogeneous valuation ${\mathfrak {v}}: R \setminus \{0\} \to {\mathbb {Z}}^d$ of rank $d$ such that the associated graded $\operatorname {gr}_{\mathfrak {v}}(R)$ is finitely generated. This then implies that any polarized $d$-dimensional projective variety $X$ has a flat deformation over ${\mathbb {A}}^1$, with reduced and irreducible fibers, to a polarized projective complexity-one $T$-variety (i.e., a variety with a faithful action of a $(d-1)$-dimensional torus $T$). As an application we conclude that any $d$-dimensional complex smooth projective variety $X$ equipped with an integral Kähler form has a proper $(d-1)$-dimensional Hamiltonian torus action on an open dense subset that extends continuously to all of $X$.
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Dissertations / Theses on the topic "Positively homogeneous Hamiltonians"

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Garrione, Maurizio. "Existence and multiplicity of solutions to boundary value problems associated with nonlinear first order planar systems." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4930.

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The monograph is devoted to the study of nonlinear first order systems in the plane where the principal term is the gradient of a positive and positively 2-homogeneous Hamiltonian (or the convex combination of two of such gradients). After some preliminaries about positively 2-homogeneous autonomous systems, some results of existence and multiplicity of T-periodic solutions are presented in case of bounded or sublinear nonlinear perturbations. Our attention is mainly focused on the occurrence of resonance phenomena, and the corresponding results rely essentially on conditions of Landesman-Lazer or Ahmad-Lazer-Paul type. The techniques used are predominantly topological, exploiting the theory of coincidence degree and the use of the Poincaré-Birkhoff fixed point theorem. At the end, other boundary conditions, including the Sturm-Liouville ones, are taken into account, giving the corresponding existence and multiplicity results in a nonresonant situation via the shooting method and topological arguments.
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