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.
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页码：447 / 468
页数：22
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