Bifurcation of sign-changing solutions for one-dimensional p-Laplacian with a strong singular weight; p-sublinear at ∞

被引：17

作者：

Kajikiya, Ryuji ^{[2
]}

Lee, Yong-Hoon ^{[1
]}

Sim, Inbo ^{[1
]}

机构：

[1] Pusan Natl Univ, Dept Math, Pusan 609735, South Korea

[2] Nagasaki Inst Appl Sci, Nagasaki 8510193, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 3-4期

关键词：

p-Laplace equation; Singular weight; Leray-Schauder degree; Bifurcation; Positive solutions; Sign-changing solutions; MULTIPLE POSITIVE SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; DIFFERENTIAL-EQUATIONS; EIGENVALUE; EXISTENCE;

D O I：

10.1016/j.na.2008.11.056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider one-dimensional p-Laplacian problems with a singular weight which may not be in L-1. Using the properties of eigenfunctions and the global bifurcation theory, we prove existence, uniqueness, nonexistence and multiplicity results of positive solutions as well as sign-changing solutions specially when the nonlinear term is p-linear near 0 and p-sublinear at infinity. (C) 2008 Elsevier Ltd. All rights reserved.

引用

收藏

页码：1235 / 1249

页数：15

相关论文

共 25 条

[1] Eigenvalues and the one-dimensional p-Laplacian [J].

Agarwal, RP ;

Lü, HS ;

O'Regan, D .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 266 (02) :383-400

[2] A relation between two classes of indefinite weights in singular one-dimensional p-Laplacian problems [J].

Byun, Jisoo ;

Sim, Inbo .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2007, 10 (04) :889-894

[3] A HOMOTOPIC DEFORMATION ALONG P OF A LERAY-SCHAUDER DEGREE RESULT AND EXISTENCE FOR (/U'/P-2U')'+F(T,U)=O, U(O)=U(T)=O, P-GREATER-THAN-1 [J].

DELPINO, M ;

ELGUETA, M ;

MANASEVICH, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 80 (01) :1-13

[4]

Diemling K., 1987, NONLINEAR FUNCTIONAL

[5]

DRABEK P, 1992, SOLVABILITY BIFURCAT

[6] Twin positive solutions for the one-dimensional p-Laplacian boundary value problems [J].

He, XM ;

Ge, WG .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (07) :975-984

[7] On an eigenvalue problem involving the one-dimensional p-Laplacian [J].

Huy, NB ;

Thanh, TD .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 290 (01) :123-131

[8] One-dimensional p-Laplacian with a strong singular indefinite weight, I.: Eigenvalue [J].

Kajikiya, Ryuji ;

Lee, Yong-Hoon ;

Sim, Inbo .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (08) :1985-2019

[9] Multiple positive solutions for the one-dimensional p-Laplacian [J].

Kong, LB ;

Wang, JY .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 42 (08) :1327-1333

[10] A Picone-type identity and Sturmian comparison and oscillation theorems for a class of half-linear partial differential equations of second order [J].

Kusano, T ;

Jaros, J ;

Yoshida, N .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2000, 40 (1-8) :381-395