A loop type component in the non-negative solutions set of an indefinite elliptic problem

Abstract

We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with a homogeneous Neumann boundary condition. This result complements our previous results obtained in [12], where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory, rescaling and regularizing arguments, a priori bounds, and Whyburn's topological method. A further investigation of the loop type component established in [12] is also provided.