POSITIVE SOLUTION CURVES OF AN INFINITE SEMIPOSITONE PROBLEM

In this article we consider the infinite semipositone problem -Delta u= lambda f(u) in Omega, a smooth bounded domain in R-N, and u = 0 on partial derivative Omega, where f(t) = t(q) - t(-beta) and 0 < q, beta< 1. Using stability analysis we prove the existence of a connected branch of maximal solutions emanating from infinity. Under certain additional hypothesis on the extremal solution at lambda= Lambda we prove a version of Crandall-Rabinowitz bifurcation theorem which provides a multiplicity result for lambda is an element of (Lambda,Lambda + epsilon).