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September/October 2022 On a class of nonlocal Schrödinger equations with exponential growth
Giovanni Molica Bisci, Nguyen Van Thin, Luca Vilasi
Adv. Differential Equations 27(9/10): 571-610 (September/October 2022). DOI: 10.57262/ade027-0910-571

Abstract

We consider the following singularly perturbed Schrödinger equation involving the $ \frac Ns $-fractional Laplacian operator,$$ \varepsilon^{N}(-\Delta)_{ \frac Ns } ^{s}u+V(x)|u|^{\frac{N}{s}-2}u=f(u) \quad \text{in } \mathbb R^{N},$$where $\varepsilon$ is a positive parameter, $s\in (0,1)$, the potential $V$ is positive and away from zero, and $f$ is a Trudinger-Moser type nonlinearity. By using penalization methods andLusternik-Schnirelmann's theory, we examine existence, multiplicity and concentration of non-trivial non-negative solutions for small values of $\varepsilon$.

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Giovanni Molica Bisci. Nguyen Van Thin. Luca Vilasi. "On a class of nonlocal Schrödinger equations with exponential growth." Adv. Differential Equations 27 (9/10) 571 - 610, September/October 2022. https://doi.org/10.57262/ade027-0910-571

Information

Published: September/October 2022
First available in Project Euclid: 2 June 2022

Digital Object Identifier: 10.57262/ade027-0910-571

Subjects:
Primary: 35A15 , 35J60 , 35R11

Rights: Copyright © 2022 Khayyam Publishing, Inc.

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Vol.27 • No. 9/10 • September/October 2022
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