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论文类型：期刊论文

发表时间：2015-01-19

发表刊物：ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

收录刊物：SCIE

ISSN号：1072-6691

关键字：Homoclinic solution; Mountain pass theorem; damped differential equation; Nehari manifold

摘要：We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation
   u + c(u)overdot - L(t)u + W-u(t, u) = 0
   where L(t) and W(t, u) are neither autonomous nor periodic in t. Under certain assumptions on L and W, we obtain in finitely many homoclinic solutions when the nonlinearity W(t, u) is sub-quadratic or super-quadratic by using critical point theorems. Some recent results in the literature are generalized, and the open problem proposed by Zhang and Yuan is solved. In addition, with the help of the Nehari manifold, we consider the case where W(t, u) is indefinite and prove the existence of at least one nontrivial quasi-homoclinic solution.