English

Degenerate Schr{\"o}dinger-Kirchhoff $(p, N)$-Laplacian problem With singular Trudinger-Moser nonlinearity in $\mathbb{R}^N$

Analysis of PDEs 2023-12-04 v1

Abstract

In this paper, we deal with the existence of nontrivial nonnegative solutions for a (p,N)(p, N)-Laplacian Schr{\"o}dinger-Kirchhoff problem in RN\mathbb{R}^N with singular exponential nonlinearity. The main features of the paper are the (p,N)(p, N) growth of the elliptic operators, the double lack of compactness, and the fact that the Kirchhoff function is of degenerate type. To establish the existence results, we use the mountain pass theorem, the Ekeland variational principle, the singular Trudinger-Moser inequality, and a completely new Br\'ezis-Lieb type lemma for singular exponential nonlinearity.

Keywords

Cite

@article{arxiv.2312.00478,
  title  = {Degenerate Schr{\"o}dinger-Kirchhoff $(p, N)$-Laplacian problem With singular Trudinger-Moser nonlinearity in $\mathbb{R}^N$},
  author = {Deepak Kumar Mahanta and Tuhina Mukherjee and Abhishek Sarkar},
  journal= {arXiv preprint arXiv:2312.00478},
  year   = {2023}
}