On sign-changing solutions for nonlinear operator equations

被引：11

作者：

Li, Fuyi ^{[1
]}

Liang, Zhanping ^{[1
]}

Zhang, Qi ^{[1
]}

Li, Yuhua ^{[1
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 327卷 / 02期

关键词：

cone; fixed point index; the index of isolated zero point; e-continuous; completely continuous operator;

D O I：

10.1016/j.jmaa.2006.04.064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1010 / 1028

页数：19

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