Exact multiplicity results for a p -Laplacian problem with concave-convex-concave nonlinearities

被引：15

作者：

Addou, Idris ^{[1
]}

Wang, Shin-Hwa ^{[2
]}

机构：

[1] Ecole Polytechnique de Montreal, Dept. de Math. et de Genie Indust., Montréal, Que. H3C 3A7, Succursale Centre-Ville

[2] Department of Mathematics, National Tsing Hua University

来源：

Nonlinear Analysis, Theory, Methods and Applications | 2003年 / 53卷 / 01期

关键词：

Bifurcation; Concave-convex-concave nonlinearity; Dead-core solution; Exact multiplicity result; p-Laplacian; Positive solution; Time-map;

D O I：

10.1016/S0362-546X(02)00298-5

中图分类号：

学科分类号：

摘要：

We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case p=2 as well as the case p > 1, when the nonlinearity f satisfies f(0)=0 and has two distinct simple positive zeros and such that f″ changes sign exactly twice on (0,∞). Note that we may allow that f″ changes sign more than twice on (0,∞). Some interesting examples of quartic polynomials are given. In particular, for f(u)=-u2(u-1)(u-2), we study the evolution of the bifurcation curves of the p-Laplacian problem as p increases from 1 to infinity, and hence are able to determine the exact multiplicity of positive solutions for each p > 1. © 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：111 / 137

页数：26

共 16 条

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