Degenerate Schrödinger–Kirchhoff (p, N)-Laplacian problem with singular Trudinger–Moser nonlinearity in RN

In this paper, we deal with the existence of nontrivial nonnegative solutions for a (p, N)-Laplacian Schrödinger-Kirchhoff problem in ℝN with singular exponential nonlinearity. The main features of the paper are the (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 Brézis-Lieb-type lemma for singular exponential nonlinearity. © 2024 Walter de Gruyter GmbH, Berlin/Boston.