Positive solutions of semipositone elliptic problems with critical Trudinger-Moser nonlinearities

Kanishka Perera, Inbo Sim

Abstract


We prove the existence of a positive solution to a semipositone $N$-Laplacian problem with a critical Trudinger-Moser nonlinearity. The proof is based on obtaining uniform $C^{1,\alpha}$ a priori estimates via a compactness argument. Our result is new even in the semilinear case $N = 2$, and our arguments can easily be adapted to obtain positive solutions of more general semipositone problems with critical Trudinger-Moser nonlinearities.

Keywords


Semipositone $N$-Laplacian problems; critical Trudinger-Moser nonlinearities; positive solutions; uniform $C^{1;\alpha}$ a priori estimates

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