On positive solutions for a class of infinite semipositone problems

Document Type: Research Paper

Authors

1 Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

2 Department of Mathematics, Faculty of Basic Sciences, Payame Noor University, Tehran, Iran

Abstract

We discuss the existence of a positive solution to the in nite semipositone problem
􀀀u = au 􀀀 bu
 􀀀 f(u) 􀀀
c
u ; x 2
; u = 0; x 2 @
;
where  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.

Keywords