A class of semipositone p-Laplacian problems with a critical growth reaction term

Abstract

We prove the existence of ground state positive solutions for a class of semipositone p-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform C1,α a priori estimates and by concentration compactness arguments. Our results are new even in the semilinear case p = 2.

Keywords

• critical semipositone p-laplacian problems
• ground state positive solutions
• concentration compactness
• uniform c1,α a priori estimates
• primary 35b33
• secondary 35j92
• 35b09
• 35b45