POSITIVE SOLUTIONS FOR A CLASS OF INFINITE SEMIPOSITONE PROBLEMS INVOLVING THE p- LAPLACIAN OPERATOR

We discuss the existence of a positive solution to the infinite semipositone problem -Delta(u)(p) = au(p-1) - bu(gamma) - f (u) - c/u(alpha), x is an element of Omega, u = 0; x is an element of partial derivative Omega; where Delta(p) is the p-Laplacian operator, p > 1, g > p 1, a 2 (0, 1), a, b and c are positive constants, Omega is a bounded domain in R-N with smooth boundary partial derivative Omega, and f : [ 0, infinity) -> R is a continuous function such that f (u) -> infinity as u -> infinity. Also we assume that there exist A > 0 and beta > p - 1 such that f (s) < As-beta, for all s > 0. We obtain our result via the method of sub- and supersolutions.