Results 21 to 30 of about 697 (183)
Homoclinic Solutions for Fourth Order Traveling Wave Equations [PDF]
SIAM Journal on Mathematical Analysis, 2009 We consider homoclinic solutions of fourth order equations $$ u^{""} + ^2 u^{"} + V_u (u)=0 {in} \R ,$$ where $V(u)$ is either the suspension bridge type $V(u)=e^u-1-u$ or Swift-Hohenberg type $ V(u)= {1/4}(u^2-1)^2$. For the suspension bridge type equation, we prove existence of a homoclinic solution for {\em all} $ \in (0, _*)$ where $ _ ...
Santra, Sanjiban, Wei, Juncheng
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Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems
Abstract and Applied Analysis, 2013 We establish a new existence result on homoclinic solutions for a second-order nonperiodic Hamiltonian systems. This homoclinic solution is obtained as a limit of solutions of a certain sequence of nil-boundary value problems which are obtained by the ...
Qiang Zheng
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Homoclinic Solutions of Hamiltonian Systems with Symmetry
Journal of Differential Equations, 1999 Consider a Hamiltonian system with a Hamiltonian of the following form: \[ H(z,t)=\tfrac{1}{2}Az\cdot z+F(z,t). \] The authors show that if (i) the spectrum of the matrix \(JA\) (where \(J\) is the standard symplectic matrix) does not intersect the imaginary axis; (ii) \(F\) is invariant under the action of a compact Lie group; and (iii) \(F\) is ...
ARIOLI, GIANNI, A. Szulkin
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On Existence of Infinitely Many Homoclinic Solutions
Monatshefte f�r Mathematik, 2000 Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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Multiple homoclinic solutions for a one-dimensional Schrödinger equation [PDF]
Discrete & Continuous Dynamical Systems - S, 2016 This paper is dedicated to the study of the problem of existence of homoclinic solutions to a Schrödinger equation of the form \[ x''-V(t)x+x^3=0,\eqno{(1)} \] where \(V:\mathbb R\to\mathbb R\) is a \(L^1\)-function.
DAMBROSIO, Walter, D. Papini
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Center Manifolds for Homoclinic Solutions
Journal of Dynamics and Differential Equations, 2000 In this article, center-manifold theory for homoclinic solutions of ordinary differential equations or semilinear parabolic equations is developed. Here, a center manifold along a homoclinic orbit q(t) is a locally invariant manifold containing all solutions which stay close to q(t) in phase space for all times. Therefore, as usual, the low-dimensional
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Homoclinic solutions for a class of non-periodic second order Hamiltonian systems
Electronic Journal of Qualitative Theory of Differential Equations, 2010 We study the existence of homoclinic solutions for the second order Hamiltonian system $\ddot{u}+V_{u}(t,u)=f(t)$. Let $V(t,u)=-K(t,u)+W(t,u)\in C^{1}(\mathbb{R}\times\mathbb{R}^{n}, \mathbb{R})$ be $T$-periodic in $t$, where $K$ is a quadratic growth ...
Jian Ding, Junxiang Xu, Fubao Zhang
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Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems
Abstract and Applied Analysis, 2013 This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a ...
Jingli Xie, Zhiguo Luo, Guoping Chen
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Global bifurcation of homoclinic solutions of Hamiltonian systems
Discrete & Continuous Dynamical Systems - A, 2003 We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
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Variational Approach to Impulsive Problems: A Survey of Recent Results
Abstract and Applied Analysis, 2014 We present a survey on the existence of nontrivial solutions to impulsive differential equations by using variational methods, including solutions to boundary value problems, periodic solutions, and homoclinic solutions.
Fang-fang Liao, Juntao Sun
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