## Topological Methods in Nonlinear Analysis

### On an asymptotically linear singular boundary value problems

Dinh Dang Hai

#### 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

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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