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Multi-bump solutions for singularly perturbed Schrödinger equations in $\mathbb{R}^2$ with general nonlinearities

Object's details: Multi-bump solutions for singularly perturbed Schrödinger equations in $\mathbb{R}^2$ with general nonlinearities

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Provider:Akademicka Platforma Czasopism

Description

Title:
Multi-bump solutions for singularly perturbed Schrödinger equations in $\mathbb{R}^2$ with general nonlinearities
Creator:
Cassani, Daniele;
do Ó, João Marcos;
Zhang, Jianjun
Description:
We are concerned with the following equation: $$ -\varepsilon^2\Delta u+V(x)u=f(u),\quad u(x)> 0\quad \mbox{in } \mathbb{R}^2. $$ By a variational approach, we construct a solution $u_\varepsilon$ which concentrates, as $\varepsilon \to 0$, around arbitrarily given isolated local minima of the confining potential $V$: here the nonlinearity $f$ has a quite general Moser's critical growth, as in particular we do not require the {\it monotonicity} of $f(s)/s$ nor the {\it Ambrosetti-Rabinowitz} condition.
Object availability:
free access
Rights:
Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
Date:
2016.10.27
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 49, No 1 (March 2017); 205 - 231;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.074/10297 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.074/10298
Subject:
Semiclassical states;
Schrödinger equations;
critical growth;
35B25;
35B33;
35J61
Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.074
Data provider:
Akademicka Platforma Czasopism

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