Existence of solution for a nonlinear fifth-order three-point boundary value problem

Zouaoui Bekri, S. Benaicha
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引用次数: 6

Abstract

In this paper, we study the existence of nontrivial solution for the fourth-order three- point boundary value problem having the following form u(4) (t) + f (t, u(t)) = 0, 0 < t < 1, u(0) = α(η), u'(0) = u''(0) = 0, u(1) = βu(η), where η ∈ (0, 1), α, β ∈ R, f ∈ C ([0, 1] × R, R). We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. And by using the Leray-Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an application, we also given some examples to illustrate the results obtained.
一类非线性五阶三点边值问题解的存在性
本文研究了具有如下形式的四阶三点边值问题非平凡解的存在性:u(4) (t) + f (t, u(t)) = 0,0 < t < 1, u(0) = α(η), u'(0) = u'(0) = 0, u(1) = βu(η),其中η∈(0,1),α, β∈R, f∈C ([0,1] × R, R),给出了非平凡解的存在性的充分条件。利用Leray-Schauder非线性替代证明了所提问题至少有一个解的存在性。作为应用,我们还给出了一些例子来说明所得到的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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