Topological Methods in Nonlinear Analysis

On an asymptotically linear singular boundary value problems

Dinh Dang Hai

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Abstract

We prove the existence of positive solutions for the singular boundary value problems $$ \begin{cases} \displaystyle -\Delta u=\frac{p(x)}{u^{\beta }}+\lambda f(u) & \text{in }\Omega , \\ u=0 &\text{on }\partial \Omega , \end{cases} $$ where $\Omega $ is a bounded domain in $\mathbb{R}^n$ with smooth boundary $\partial \Omega$, $0< \beta < 1$, $\lambda > 0$ is a small parameter, $f\colon (0,\infty )\rightarrow \mathbb{R}$ is asymptotically linear at $\infty$ and is possibly singular at $0$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 39, Number 1 (2012), 83-92.

Dates
First available in Project Euclid: 20 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461184855

Mathematical Reviews number (MathSciNet)
MR2934335

Zentralblatt MATH identifier
06077278

Citation

Hai, Dinh Dang. On an asymptotically linear singular boundary value problems. Topol. Methods Nonlinear Anal. 39 (2012), no. 1, 83--92. https://projecteuclid.org/euclid.tmna/1461184855


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