Nontrivial solution of a nonlinear second-order three-point boundary value problem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Nontrivial solution of a nonlinear second-order three-point boundary value problem

Authors:

Affiliation:

(1) Department of Mathematics, Lishui University, Lishui, 323000, China;(2) Department of Applied Mathematics, Zhejiang Sci-Tec University, Hangzhou, 310018, China;(3) Department of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, 310018, China

Abstract:

In this paper, for a second-order three-point boundary value problem

$$begin{gathered} u' + f(t,u) = 0, 0 < t < 1, hfill au(0) - bu'(0) = 0, u(1) - alpha u(eta ) = 0, hfill end{gathered} $$

where η ∈ (0, 1), a, b, α ∈ R with a ² + b ² > 0, the existence of its nontrivial solution is studied. The conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given. This work was supported by Key Academic Discipline of Zhejiang Province of China(2005), the Natural Science Foundation of Zhejiang Province of China (Y605144) and the Education Department of Zhejiang Province of China(20051897).

Keywords:

three-point boundary value problem nonlinear alternative of Leray-Schauder nontrivial solution

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