Positive solutions for semipositone (p,N)-Laplacian problems with critical Trudinger-Moser nonlinearities

作者：Zhang, Yuanyuan; Yang, Yang^*

来源：Revista Matematica Complutense, 2022, 35(1): 133-146.

DOI：10.1007/s13163-021-00386-y

• (p, N)-Laplacian
• Critical Trudinger-Moser nonlinearities
• Variational methods
• Positive solutions
• Semipositone problems

In this paper, we deal with the existence of positive solutions for semipositone (p, N)-Laplacian problems with critical Trudinger-Moser nonlinearities in a bounded domain: @@@ {-Delta(p)u -Delta(N) u =lambda u(N-1)e(ss uN') - mu, in Omega; @@@ u > 0, in Omega; @@@ u = 0, on partial derivative Omega. @@@ We obtain the positive solutions by combining variational methods with regularity arguments. And the main novelty here is to obtain a uniform C-1,C-alpha priori estimate of the weak solution. Our arguments can be also adapted to seek positive solutions of more general semipositone problems.

• 单位
  江南大学