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

共 50 条

[41] Existence of sign-changing solutions for the p-Laplacian equation from linking type theorem
Wang, You Jun
Shen, Yao Tian
[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2010, 26 (07) : 1355 - 1368
[42] Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
Yuanze Wu
Yisheng Huang
[J]. Boundary Value Problems, 2013
[43] Three positive solutions for one-dimensional p-Laplacian problem with sign-changing weight
Sim, Inbo
Tanaka, Satoshi
[J]. APPLIED MATHEMATICS LETTERS, 2015, 49 : 42 - 50
[44] Infinitely many sign-changing solutions for p-Laplacian equation involving the critical Sobolev exponent
Wu, Yuanze
Huang, Yisheng
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[45] PRINCIPAL EIGENVALUES FOR THE FRACTIONAL p-LAPLACIAN WITH UNBOUNDED SIGN-CHANGING WEIGHTS
Asso, Oumarou
Cuesta, Mabel
Doumate, Jonas Tele
Leadi, Liamidi
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 2023 (38)
[46] Sign-changing solutions for a class of p-Laplacian Kirchhoff-type problem with logarithmic nonlinearity
Li, Ya-Lei
Wang, Da-Bin
Zhang, Jin-Long
[J]. AIMS MATHEMATICS, 2020, 5 (03): : 2100 - 2112
[47] Existence results of sign-changing solutions for singular one-dimensional p-Laplacian problems
Lee, Yong-Hoon
Sim, Inbo
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (05) : 1195 - 1209
[48] The Brezis-Nirenberg type problem for the p-Laplacian: infinitely many sign-changing solutions
He, Tieshan
He, Lang
Zhang, Meng
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (03)
[49] The Brézis–Nirenberg type problem for the p-Laplacian: infinitely many sign-changing solutions
Tieshan He
Lang He
Meng Zhang
[J]. Calculus of Variations and Partial Differential Equations, 2020, 59
[50] Existence of multiple solutions for nonhomogeneous Schrodinger-Kirchhoff system involving the fractional p-Laplacian with sign-changing potential
Chen, Jianhua
Huang, Xianjiu
Zhu, Chuanxi
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 77 (10) : 2725 - 2739

← 1 2 3 4 5 →