Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation

Existence of homoclinic orbits for asymptotically periodic systems involving Duffing-like equation

we are concerned with perturbations of the Hamiltonian system of the type c L(t)q + W&, q) = 0, t E R, WI where q = (ql, , qN) E WN, W E C1(W x WN,R), and L(t) E C(W,WN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). @ 2003 Elsevier Science Ltd. All rights reserved. KeywordsHomoclinic orbits, Duffing equat...

Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian

and Applied Analysis 3 W4 W̃ n, x ∇W n, x , x − pW n, x , lim |x|→∞ W̃ n, x ∞ uniformly for n ∈ Z, 1.7 and for any fixed 0 < c1 < c2 < ∞, inf n∈Z, c1≤|x|≤c2 W̃ n, x |x| > 0. 1.8 Then problem 1.1 has at least one nontrivial homoclinic solution. Remark 1.2. The function W n, x in this paper is asymptotically p-linear at infinity. The behavior of the gradient of W n, x at infinity is like that of a f...

Existence of Periodic Solutions for the Duffing Equation with Impulses

Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

and Applied Analysis 3 We make the following assumptions. A1 W t, z ∈ C1 R × R2N,R is 1-periodic in t. W t, 0 0 for all t ∈ R. There exist constants c1 > 0 and μ > 2 such that Wz t, z z ≥ c1|z| for t, z ∈ R × R2N. A2 there exist c2, r > 0 such that |Wz t, z | ≤ c2|z|μ−1 for t ∈ R and |z| ≤ r. A3 there exist c3, R ≥ r and p ≥ μ such that |Wz t, z | ≤ c3|z|p−1 for t ∈ R and |z| ≥ R. A4 there exis...

Existence of Periodic Solutions for a Class of Asymptotically p-Linear Discrete Systems Involving p-Laplacian