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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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
Christian Pötzsche, Robert Skiba
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Fast homoclinic solutions for damped vibration problems under local conditions [PDF]
Journal of Inequalities and ApplicationsIn this paper, we study the fast homoclinic solutions for the following damped vibration problems u ¨ ( t ) + q ( t ) u ˙ ( t ) − L ( t ) u ( t ) + ∇ W ( t , u ( t ) ) = 0 $\ddot{u}(t)+q(t)\dot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0$ , ∀ t ∈ R $\forall t \in \
Wen-Kai Li +3 more
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Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations [PDF]
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
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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 n-dimensional p-Laplacian neutral differential systems with a time-varying delay [PDF]
Advances in Difference Equations, 2018 In this paper, we investigate the existence of a set with 2kT $2kT$-periodic solutions for n-dimensional p-Laplacian neutral differential systems with a time-varying delay (φp(u(t)−Cu(t−τ))′)′+ddt∇F(u(t))+G(u(t−γ(t)))=ek(t) $(\varphi_{p}(u(t)-Cu(t-\tau ))
Fang Gao, Wenbin Chen
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Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential
Entropy, 2017 In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville–Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the ...
Neamat Nyamoradi +3 more
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Bifurcation of Homoclinic Solutions for Hamiltonian Systems
Zeitschrift für Analysis und ihre Anwendungen, 2002 We consider the Hamiltonian system Ju'(x) + Mu(x) – \bigtriangledown _u F(x,u(x)) = \lambda u(x). Using variational methods obtained by Stuart on the one hand and by Giacomoni and Jeanjean on the other, we get bifurcation results for homoclinic solutions by imposing ...
Robert Joosten
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Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. [PDF]
ScientificWorldJournal, 2014 Sun G, Mai A.
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Existence and multiplicity of homoclinic solutions for a difference equation
Electronic Journal of Differential Equations, 2020 The aim of this article is to obtain homoclinic solutions for a discrete problem involving p-Laplacian. We prove the existence of at least one, two and three solutions for the problem. Our approach is based on variational methods.
Shapour Heidarkhani +2 more
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