Positive solutions of a focal problem for one-dimensional p-Laplacian equations

被引：11

作者：

Yang, Zhilin ^{[1
]}

O'Regan, Donal ^{[2
]}

机构：

[1] Qingdao Technol Univ, Dept Math, Qingdao, Shandong, Peoples R China

[2] Natl Univ Ireland, Dept Math, Galway, Ireland

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2012年 / 55卷 / 7-8期

关键词：

p-Laplacian equation; Positive solution; Focal problem; Fixed point index; Dirichlet problem; Jensen's inequality; BOUNDARY-VALUE-PROBLEMS; EXISTENCE;

D O I：

10.1016/j.mcm.2011.11.052

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper mainly deals with the existence and multiplicity of positive solutions for the focal problem involving both the p-Laplacian and the first order derivative: {((u')(p-1))' + f (t, u, u') = 0, t is an element of(0, 1), u(0) = u'(1) = 0. The main tool in the proofs is the fixed point index theory, based on a priori estimates achieved by using Jensen's inequality and a new inequality. Finally the main results are applied to establish the existence of positive symmetric solutions to the Dirichlet problem: {(|u'|(p-2)u')' + f (u, u') = 0, t is an element of (-1, 0) boolean OR (0, 1), u(-1) = u(1) = 0. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1942 / 1950

页数：9

共 50 条

[31] Existence and multiplicity of positive solutions for one-dimensional p-Laplacian problem with sign-changing weight [J].

Miao, Liangying ;

Xu, Man ;

He, Zhiqian .

ELECTRONIC RESEARCH ARCHIVE, 2023, 31 (06) :3086-3096

[32] Positive solutions for one-dimensional third-order p-Laplacian boundary value problems [J].

Yan Sun .

Advances in Difference Equations, 2017

[33] Positive solutions for one-dimensional p-Laplacian boundary value problems with sign changing nonlinearity [J].

Ji, Dehong ;

Tian, Yu ;

Ge, Weigao .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (11) :5406-5416

[34] Positive solutions for one-dimensional third-order p-Laplacian boundary value problems [J].

Sun, Yan .

ADVANCES IN DIFFERENCE EQUATIONS, 2017,

[35] Multiple positive solutions of singular eigenvalue type problems involving the one-dimensional p-Laplacian [J].

Sánchez, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 292 (02) :401-414

[36] Positive solutions for a multi-point eigenvalue problem involving the one dimensional p-Laplacian [J].

Wang, Youyu ;

Ge, Weigao ;

Cheng, Sui Sun .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2009, (40) :1-13

[37] STUDIES ON NBVPS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN [J].

Liu, Yuji .

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2011, 73 (04) :53-70

[38] Positive solutions for a fourth order p-Laplacian boundary value problem [J].

Xu, Jiafa ;

Yang, Zhilin .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (07) :2612-2623

[39] CAUCHY PROBLEM FOR ONE-DIMENSIONAL P-LAPLACIAN EQUATION WITH POINT SOURCE [J].

Li Yinghua ;

Ke Yuanyuan ;

Wang Zejia .

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2005, 18 (01) :22-34

[40] EXISTENCE RESULTS FOR POSITIVE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN [J].

Liu, Yuji .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (01) :135-163

← 1 2 3 4 5 →