A class of semipositone $p$-Laplacian problems with a critical growth   reaction term
  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 $C^{1,\alpha}$ a priori estimates and by concentration compactness arguments. Our results are new even in the semilinear case $p = 2$. 
Kanishka Perera, Ratnasingham Shivaji, Inbo Sim
math.AP