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

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