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    188宝金博页面版: Existence of two almost homoclinic solutions for p ( t )-Laplacian Hamiltonian systems with a small perturbation

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    内容提示： J. Appl. Math. Comput. (2016) 52:173–189DOI 10.1007/s12190-015-0936-0ORIGINAL RESEARCHExistence of two almost homoclinic solutionsfor p(t)-Laplacian Hamiltonian systemswith a small perturbationZiheng Zhang 1 · Rong Yuan 2Received: 16 May 2015 / Published online: 23 September 2015? Korean Society for Computational and Applied Mathematics 2015Abstract In this paper we study the existence of two almost homoclinic solutions forthe following second order p(t)-Laplacian Hamiltonian systems with a small pertur...

    文档格式：PDF | 页数：17 | 浏览次数：489 | 上传日期：2018-03-15 21:13:38 | 文档星级：
    J. Appl. Math. Comput. (2016) 52:173–189DOI 10.1007/s12190-015-0936-0ORIGINAL RESEARCHExistence of two almost homoclinic solutionsfor p(t)-Laplacian Hamiltonian systemswith a small perturbationZiheng Zhang 1 · Rong Yuan 2Received: 16 May 2015 / Published online: 23 September 2015© Korean Society for Computational and Applied Mathematics 2015Abstract In this paper we study the existence of two almost homoclinic solutions forthe following second order p(t)-Laplacian Hamiltonian systems with a small pertur-bationddt? |˙ u(t)| p(t)−2˙ u(t) ? − a(t)|u(t)| p(t)−2 u(t) + ∇W(t,u(t)) = f (t),where t ∈ R, u ∈ R n , p ∈ C(R,R) with p(t) > 1, a ∈ C(R,R), W ∈ C 1 (R ×R n ,R) and ∇W(t,u) is the gradient of W(t,u) at u, f ∈ C(R,R n ) and belongs toL q(t) (R,R n ). The point is that, assuming that a(t) is bounded in the sense that thereare two constants 0 < τ 1 < τ 2 < ∞ such that τ 1 ≤ a(t) ≤ τ 2 for all t ∈ R, W(t,u) isofsuper-p(t)growth as |u| → ∞and satisf i essome other reasonable hypothesis, f issuff i cientlysmallin L q(t) (R,R n ),weprovideonenewcriteriontoensuretheexistenceof two almost homoclinic solutions. Recent results in the literature are extended andsignif i cantly improved.Keywords Homoclinic solutions · Critical point · Variational methods · Mountainpass theoremMathematics Subject Classif i cation 34C37 · 35A15 · 35B38B Ziheng Zhangzhzh@mail.bnu.edu.cnRong Yuanryuan@bnu.edu.cn1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China2Department of Mathematical Sciences, Beijing Normal University, Beijing 100875, China123

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