Positive solutions for a fourth-order three-point BVP with sign-changing Green's function
Positive solutions for a fourth-order three-point BVP with sign-changing Green's function
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具有变号格林函数的四阶三点 BVP 的正解
DOI：
10.14232/ejqtde.2018.1.5
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发表时间：
2018-01-01
影响因子：
1.1
通讯作者：
Zhao, Juan
中科院分区：
文献类型：
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作者：
Zhang, Yun;Sun, Jian-Ping;Zhao, Juan
本文关注如下四阶三点边值问题{u((4))(t) = f(t, u(t))，t是[0, 1]中的元素，u'(0) = u ''(0) = u '''(eta) = u(1) = 0，其中eta是[1/3, 1)中的元素。尽管格林函数改变了符号，对于任意正整数n（>= 2），通过对f施加一些合适的条件，我们仍然获得上述问题的至少n - 1个递减正解的存在性。使用的主要工具是不动点指数理论。
This paper is concerned with the following fourth-order three-point boundary value problem{u((4))(t) = f(t, u(t)), t is an element of [0, 1],u'(0) = u ''(0) = u '''(eta) = u(1) = 0,where eta is an element of [1/3, 1). In spite of sign-changing Green's function, for arbitrary positive integer n (>= 2), we still obtain the existence of at least n - 1 decreasing positive solutions to the above problem by imposing some suitable conditions on f. The main tool used is the fixed point index theory.