On positive solutions for a class of infinite semipositone problems

We discuss the existence of a positive solution to the innite semipositone problem\Delta u=au-bu^\gamma-f(u)-\frac{c}{u^\alpha}, \quad x\in\Omega,\quad u=۰, x\in\partial\Omega,where \Delta is the Laplacian operator,  \gamma>۱, \alpha\in(۰,۱), a,b and c are positive constants, \Omega is a bounded domain in \mathbb{R}^N with smooth boundary \partial\Omega, and f : [۰;۱) \to \mathbb{R} is a continuous function such that f(u)\to \infty as u\to \infty. Also we assume that there exist A > ۰ and \beta > ۱ such that f(s) \leq As^\beta, for all s \geq ۰. We obtain our result via the method of sub- and supersolutions.

Keywords:

positive solution , Innite semipositone , Sub- and supersolutions