Positive solutions of semipositone elliptic problems with critical Trudinger-Moser nonlinearities
Słowa kluczowe
Semipositone $N$-Laplacian problems, critical Trudinger-Moser nonlinearities, positive solutions, uniform $C^{1, \alpha}$ a priori estimatesAbstrakt
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.Bibliografia
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