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Infinitely many homoclinic orbits for a class of second‐order damped differential equations
Authors:Chuanfang Zhang  Zhiqing Han
Affiliation:1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China;2. Collage of Science, Heilongjiang University of Science and Technology, Harbin, China
Abstract:We investigate the existence and multiplicity of homoclinic orbits for the second‐order damped differential equations For Equation 1 where L(t) and W(t,u) are neither autonomous nor periodic in t. Under certain assumptions on g, L, and W, we get infinitely many homoclinic orbits for superquadratic, subquadratic and concave–convex nonlinearities cases by using fountain theorem and dual fountain theorem in critical point theory. These results generalize and improve some existing results in the literature. Copyright © 2015 JohnWiley & Sons, Ltd.
Keywords:homoclinic orbit  fountain theorem  dual fountain theorem  damped differential equation  subclass34C37  35A15  37J45
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