Existence and nonexistence results for quasilinear semipositone Dirichlet problems

Abstract

We use the sub/supersolution method to analyze a semipositone Dirichlet problem for the p-Laplacian. To find a positive solution, we therefore focus on a related problem that produces positive subsolutions. We establish a new nonexistence result for this subsolution problem on general domains, discuss the existence of positive radial subsolutions on balls, and then apply our results to problems involving particular semipositone nonlinearities.

Keywords

• semipositone problems
• p-Laplacian
• positive solutions