A Lane-Emden-Fowler type problem with singular nonlinearity

Abstract

The main purpose of this article is to establish the existence result concerning to the problem $-\Delta u(x)+c(x)u(x)=a(x)f(u(x))$, $x\in \mathbb{R}^{N}$, $N>2$, $u(x)\rightarrow 0$ as $\left\vert x\right\vert \rightarrow \infty$. Similary problems have been also studied. The proofs of the existence are based on the maximum principle and sub and super solutions method.