On Positive Solutions for Semilinear Elliptic Equations with an Indefinite Nonlinearity Via Bifurcation

Abstract

Existence of a positive solution was establsihed via bifurcation theory for sernilinear elliptic boundary value problems. With the aid of maximum principles and a priori estimates, global behavior of the bifurcation curve was obtained. In particular, a general sufficient condition was given for existence of multiple positive solutions when the nonlinearity is sub-critical and indefinite.