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2021 Quasilinear Schrödinger equations with singular and vanishing potentials involving nonlinearities with critical exponential growth
Yane Lísley Araújo, Gilson Carvalho, Rodrigo Clemente
Topol. Methods Nonlinear Anal. 57(1): 317-342 (2021). DOI: 10.12775/TMNA.2020.024

Abstract

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.

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Yane Lísley Araújo. Gilson Carvalho. Rodrigo Clemente. "Quasilinear Schrödinger equations with singular and vanishing potentials involving nonlinearities with critical exponential growth." Topol. Methods Nonlinear Anal. 57 (1) 317 - 342, 2021. https://doi.org/10.12775/TMNA.2020.024

Information

Published: 2021
First available in Project Euclid: 5 March 2021

Digital Object Identifier: 10.12775/TMNA.2020.024

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 1 • 2021
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