A Variational Approach to Superlinear Semipositone Elliptic Problems

In this paper we present a variational approach to a class of elliptic problems with superlinear semipositone nonlinearities. We consider the parametrized family of problems (Formula presented) with l > 0, a continuous, and f subcritical and superlinear at infinity. We obtain positive solutions of such problems for 0 < λ < λ0 by combining a suitable rescaling with a continuity argument. In doing so, we require f to be of regular variation at infinity, so that f does not need to be asymptotic to a power. Furthermore, a may vanish in open parts of Ω or change sign. © 2016 American Mathematical Society.