On sign-changing and multiple solutions of the p-Laplacian

被引：52

作者：

Zhang, ZT ^{[1
]}

Li, SJ ^{[1
]}

机构：

[1] Acad Sinica, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 197卷 / 02期

关键词：

critical points; p-Laplacian; sign-changing solutions; multiple solutions; jumping nonlinearities;

D O I：

10.1016/S0022-1236(02)00103-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we construct the pseudo-gradient vector field in W-0(1,p)(Omega), by which we obtain the positive and negative cones of W-0(1,p)(Omega) are both invariant sets of the descent flow of the corresponding functional. Then we use differential equations theory in Banach spaces and dynamics theory to study p-Laplacian boundary value problems with "jumping" nonlinearities at zero or infinity, and get new multiple solutions and sign-changing solutions theorems of p-Laplacian. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：447 / 468

页数：22

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