On nonlinear elliptic equations with singular lower order term.
Bull. Korean Math. Soc.
Published online November 5, 2020
Amine Marah and Hicham Redwane
FST SETTAT, Faculté des Sciences Juridiques, Economiques et Sociales Université Hassan premier faculté
Abstract : We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like
$$\left\{
\begin{aligned}
&-{\rm div}\Big((a(x)+|u|^q) \nabla u\Big)= \frac{f}{|u|^\gamma}\ \ {\rm in}\ \Omega,\\
& u=0\ \ {\rm on}\ {\partial \Omega},\\
\end{aligned}
\right.$$
where $\Omega$ is a bounded open subset of $\mathbb{R}^N (N \geq 2)$, $a(x)$ is a measurable nonnegative function, $q, \gamma> 0$ and the source $f$ is a nonnegative (not identicaly zero) function belonging to $L^m(\Omega)$ for some $m \geq 1$. Our results will depend on the summability of $f$ and on the values of $q, \gamma> 0$.
Keywords : Nonlinear singular elliptic equations, Existence, Regularity.
MSC numbers : 35J62, 35J75.
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