ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF INFINITE SEMIPOSITONE PROBLEMS

We discuss the existence of a positive solution to the infinite semipositone problem -Delta u = au + bu(2) - du(2) - f(u) - c/u(alpha), x is an element of Omega, u = 0, x is an element of partial derivative Omega where alpha is an element of (0, 1), a; b; d and c are positive constants, Omega is a bounded domain in R-N with smooth boundary partial derivative Omega, Delta is the Laplacian operator, and f : [0, infinity) -> R is a nondecreasing continuous function such that f(u) -> infinity and f(u)/u -> 0 as u -> infinity. We obtain our result via the method of sub- and supersolutions. We also extend our result to classes of infinite semipositone system and p-Laplacian problem.