Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems
Abstract and Applied Analysis, 2013 We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition ...
Xiaoping Wang
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Homoclinic orbits for a class of second-order Hamiltonian systems with concave-convex nonlinearities
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper, we study the existence of multiple homoclinic solutions for the following second order Hamiltonian systems \begin{equation*} \ddot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0, \end{equation*} where $L(t)$ satisfies a boundedness assumption which is ...
Dong-Lun Wu, Chun-Lei Tang, Xing-Ping Wu
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Homoclinic orbits of a class of second-order difference equations [PDF]
, 2012 In this paper, we apply the variational method and the spectral theory of difference operators to investigate the existence of homoclinic orbits of the second-order difference equation Δ2x(t−1)−L(t)x(t)+Vx′(t,x(t))=0 in the two cases that V(t,⋅) is ...
Shi, Yuming, Zhang, Xu
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Homoclinic solutions in periodic partial difference equations
Advances in Nonlinear AnalysisBy using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed ...
Mei Peng, Zhou Zhan, Yu Jianshe
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Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems
Abstract and Applied Analysis, 2014 We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS) where -∞
Ziheng Zhang +2 more
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Analytical study of the Lorenz system: Existence of infinitely many periodic orbits and their topological characterization. [PDF]
Proc Natl Acad Sci U S A, 2023 Pinsky T.
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Multiple homoclinic solutions for a class of autonomous singular systems in $\bold R^2$R2.
, 1998 We look for homoclinic solutions for a class of second order autonomous Hamiltonian systems in R-2 with a potential V having a strict global maximum at the origin and a finite set S subset of R-2 of singularities, namely V(x) --> -infinity as dist(x,S) --
NOLASCO, MARGHERITA, CALDIROLI P
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Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization. [PDF]
Nat Commun, 2022 Hesse J +4 more
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Periodic points and homoclinic classes
, 2007 International audienceWe prove that there is a residual subset I of Diff such that any homoclinic class of a diffeomorphism f in I having saddles of indices alpha and beta contains a dense subset of saddles of index tau for every tau in [alpha,beta] cap ...
Díaz, Lorenzo J. +9 more
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Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries
Electronic Journal of Differential Equations, 1999 This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems $$ dot{z}=JH_z(t,z) $$ without any periodicity assumption on $H$, providing that $H(t,z ...
Cheng Lee
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