Topological Methods in Nonlinear Analysis

Topological structure of the solution set of singular equations with sign changing terms under Dirichlet boundary condition

José V. Gonçalves, Marcos R. Marcial, and Olimpio H. Miyagaki

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Abstract

In this paper we establish existence of connected components of positive solutions of the equation $ -\Delta_{p} u = \lambda f(u)$ in $\Omega$, under Dirichlet boundary conditions, where $\Omega \subset \mathbb{R}^N$ is a bounded domain with smooth boundary $\partial\Omega$, $\Delta_{p}$ is the $p$-Laplacian, and $f \colon (0,\infty) \rightarrow \mathbb{R} $ is a continuous function which may blow up to $\pm \infty$ at the origin.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 1 (2016), 73-89.

Dates
First available in Project Euclid: 23 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458740730

Digital Object Identifier
doi:10.12775/TMNA.2015.091

Mathematical Reviews number (MathSciNet)
MR3469048

Zentralblatt MATH identifier
1371.35134

Citation

Gonçalves, José V.; Marcial, Marcos R.; Miyagaki, Olimpio H. Topological structure of the solution set of singular equations with sign changing terms under Dirichlet boundary condition. Topol. Methods Nonlinear Anal. 47 (2016), no. 1, 73--89. doi:10.12775/TMNA.2015.091. https://projecteuclid.org/euclid.tmna/1458740730


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