Results 71 to 80 of about 697 (183)
Fast homoclinic solutions for damped vibration problems with superquadratic potentials
Boundary Value Problems, 2018 In this paper we investigate the existence and multiplicity of homoclinic solutions for the following damped vibration problem: DS u¨+q(t)u˙−L(t)u+Wu(t,u)=0, $$ \ddot{u}+q(t) \dot{u}-L(t)u+W_{u}(t,u)=0, $$ where q:R→R $q:\mathbb{R}\rightarrow\mathbb{R ...
Xinhe Zhu, Ziheng Zhang
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Fast homoclinic solutions for damped vibration problems under local conditions
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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Homoclinic Solutions for a Class of Hamiltonian Systems
Advanced Nonlinear Studies, 2004 Abstract We consider the first order Hamiltonian system q̇ = Hp(p, q), ṗ = −Hq(p, q), (HS) where p, q : ℝ → ℝN (N ≥ 3), H ∈ C1 (ℝN × ℝN \ {e}, ℝ ) and behaves roughly like
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Multi-pulse Orbits and Homoclinic Trees in a Non-autonomous Resonant Hamiltonian System
MATEC Web of Conferences, 2016 In this study, we develop the energy-phase method to deal with the high-dimensional non-autonomous nonlinear dynamical systems. Our generalized energy-phase method applies to integrable, two-degree-of freedom non-autonomous resonant Hamiltonian systems ...
Zhou Sha, Zhang Wei, Yu Tian-jun
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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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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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Homoclinic solutions for second order Hamiltonian systems with general potentials near the origin
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
Qingye Zhang
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Abstract and Applied Analysis, 2014 We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
Liu Yang
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Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems
Boundary Value Problems, 2018 By introducing a new superquadratic condition, we obtain the existence of two nontrivial homoclinic solutions for a class of perturbed second order Hamiltonian systems which are obtained by the mountain pass theorem and Ekeland’s variational principle.
Chunhua Deng, Dong-Lun Wu
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
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