On positive solutions for a class of infinite semipositone problems

Abstract

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