Results 1 to 10 of about 658 (145)
Existence problems for homoclinic solutions
Abstract and Applied Analysis, 2002 The problem x˙=f(t,x), x(−∞)=x(+∞), where x(±∞):=limt→±∞x(t)∈ℝn, is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.
Cezar Avramescu
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Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach.
Ali Mai, Zhan Zhou
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Homoclinic and quasi-homoclinic solutions for damped differential equations
Electronic Journal of Differential Equations, 2015 We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t,u)=0, $$ where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on
Chuan-Fang Zhang, Zhi-Qing Han
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Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation [PDF]
Journal of Mahani Mathematical Research, 2023 We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed ...
Liela Soleimani, Omid RabieiMotlagh
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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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Global Continuation of Homoclinic Solutions [PDF]
Zeitschrift für Analysis und ihre Anwendungen, 2018 When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under small temporally varying perturbations. In this paper, we abandon the smallness assumption and aim to investigate the global structure of the entity of all such bounded entire
Potzsche, Christian, Skiba, Robert
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Frontiers in Physics, 2022 A class of generalized homoclinic solutions of the nonlinear Schrödinger (NLS) equation in 1+1 dimensions is studied. These are homoclinic breathers that are shown to be derivable from the ratio of Riemann theta functions for the genus-2 solutions of ...
Alfred R. Osborne
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The Nehari manifold method for discrete fractional p-Laplacian equations
Advances in Difference Equations, 2020 The aim of this paper is to investigate the multiplicity of homoclinic solutions for a discrete fractional difference equation. First, we give a variational framework to a discrete fractional p-Laplacian equation.
Xuewei Ju, Hu Die, Mingqi Xiang
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The nonlinear vibration and dispersive wave systems with extended homoclinic breather wave solutions
Open Physics, 2022 This article investigates the extended homoclinic (heteroclinic) breather wave solutions and interaction periodic and dark soliton solutions to the nonlinear vibration and dispersive wave systems.
Rao Xianqing +5 more
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Mathematics, 2022 The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
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