Infinitely many homoclinic orbits for a class of second‐order damped differential equations |
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Authors: | Chuanfang Zhang Zhiqing Han |
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Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China;2. Collage of Science, Heilongjiang University of Science and Technology, Harbin, China |
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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. |
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Keywords: | homoclinic orbit fountain theorem dual fountain theorem damped differential equation subclass34C37 35A15 37J45 |
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