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.
Citation
Kanishka Perera. Inbo Sim. "Positive solutions of semipositone elliptic problems with critical Trudinger-Moser nonlinearities." Topol. Methods Nonlinear Anal. 55 (1) 243 - 255, 2020. https://doi.org/10.12775/TMNA.2019.074