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
$$
\cases
\displaystyle
-\Delta u=\frac{p(x)}{u^{\beta }}+\lambda f(u) & \text{in }\Omega , \\
u=0 &\text{on }\partial \Omega ,
\endcases
$$
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 $0$.

Keywords


Singular; elliptic BVP; asymptotically linear

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