This paper is devoted to the magnetic nonlinear Schr"{o}dinger equation [ Big(rac{arepsilon}{i} abla-A(x)Big)^{2}u+V(x)u=f(| u|^{2})u ext{ in } mathbb{R}^{2}, ] where $arepsilon>0$ is a parameter, $V:mathbb{R}^{2} ightarrow mathbb{R}$ and $A: mathbb{R}^{2} ightarrow mathbb{R}^{2}$ are continuous functions and $f:mathbb{R} ightarrow mathbb{R}$ is a $C^{1}$ function having exponential critical growth. Under a global assumption on the potential $V$, we use variational methods and Ljusternick-Schnirelmann theory to prove existence, multiplicity, concentration, and decay of nontrivial solutions for $arepsilon>0$ small.

Semiclassical states for a magnetic nonlinear Schrödinger equation with exponential critical growth in $mathbb{R}^{2}$ / D'Avenia, Pietro; Ji, Chao. - In: JOURNAL D'ANALYSE MATHEMATIQUE. - ISSN 0021-7670. - STAMPA. - (In corso di stampa). [10.1007/s11854-023-0312-1]

Semiclassical states for a magnetic nonlinear Schrödinger equation with exponential critical growth in $mathbb{R}^{2}$

Pietro d'Avenia;
In corso di stampa

Abstract

This paper is devoted to the magnetic nonlinear Schr"{o}dinger equation [ Big(rac{arepsilon}{i} abla-A(x)Big)^{2}u+V(x)u=f(| u|^{2})u ext{ in } mathbb{R}^{2}, ] where $arepsilon>0$ is a parameter, $V:mathbb{R}^{2} ightarrow mathbb{R}$ and $A: mathbb{R}^{2} ightarrow mathbb{R}^{2}$ are continuous functions and $f:mathbb{R} ightarrow mathbb{R}$ is a $C^{1}$ function having exponential critical growth. Under a global assumption on the potential $V$, we use variational methods and Ljusternick-Schnirelmann theory to prove existence, multiplicity, concentration, and decay of nontrivial solutions for $arepsilon>0$ small.
In corso di stampa
Semiclassical states for a magnetic nonlinear Schrödinger equation with exponential critical growth in $mathbb{R}^{2}$ / D'Avenia, Pietro; Ji, Chao. - In: JOURNAL D'ANALYSE MATHEMATIQUE. - ISSN 0021-7670. - STAMPA. - (In corso di stampa). [10.1007/s11854-023-0312-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/226818
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