On positive solutions for a class of innite semipositone problems

We discuss the existence of a positive solution to the innite semipositone problem -Δ u = au - bu - f(u) -Ω c u- ; x 2 ; u = 0; x 2 @ ; where Δ is the Laplacian operator, > 1, € 2 (0; 1), a; b and c are positive constants, is a bounded domain in RN with smooth boundary @ , and f : [0;1) ! R is a continuous function such that f(u) ! 1 as u ! 1. Also we assume that there exist A > 0 and > 1 such that f(s) ≤ As, for all s ≥ 0. . We obtain our result via the method of sub- and supersolutions.