Topological Methods in Nonlinear Analysis

On singular nonpositone semilinear elliptic problems

Dinh Dang Hai

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Abstract

We prove the existence of a large positive solution for the boundary value problems $$ \begin{alignat}{2} -\Delta u &=\lambda (-h(u)+g(x,u))&\quad& \text{in }\Omega , \\ u &=0 &\quad &\text{on }\partial \Omega , \end{alignat} $$ where $\Omega $ is a bounded domain in ${\mathbb R}^{N}$, $\lambda $ is a positive parameter, $g(x,\cdot)$ is sublinear at $\infty$, and $h$ is allowed to become $\infty $ at $u=0$. Uniqueness is also considered.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 32, Number 1 (2008), 41-47.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463150461

Mathematical Reviews number (MathSciNet)
MR2466801

Zentralblatt MATH identifier
1173.35493

Citation

Hai, Dinh Dang. On singular nonpositone semilinear elliptic problems. Topol. Methods Nonlinear Anal. 32 (2008), no. 1, 41--47. https://projecteuclid.org/euclid.tmna/1463150461


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