TY - JOUR
AU - Araújo, Yane Lísley
AU - Carvalho, Gilson
AU - Clemente, Rodrigo
PY - 2021/02/08
Y2 - 2024/09/19
TI - Quasilinear Schrödinger equations with singular and vanishing potentials involving nonlinearities with critical exponential growth
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 57
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2020.024
SP - 317 - 342
AB - In this paper, we study the following class of Schrödinger equations: \[ -\Delta_{N}u+V(|x|)|u|^{N-2}u=Q(|x|)h(u) \quad \text{in } \mathbb{R}^N, \] where $N\geq 2$, $V,Q\colon \mathbb{R}^{N}\rightarrow \mathbb{R}$ are potentials that can be unbounded, decaying or vanishing at infinity and the nonlinearity $h\colon \mathbb{R}\rightarrow \mathbb{R}$ has a critical exponential growth concerning the Trudinger-Moser inequality. By using a variational approach, a version of the Trudinger-Moser inequality and a symmetric criticality type result, we obtain the existence of nonnegative weak and ground state solutions for this class of problems and under suitable assumptions, we obtain a nonexistence result.
ER -