Publication detail
SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS
RADULESCU, V. ZHANG, W. ZHANG, J.
Original Title
SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS
Type
journal article in Web of Science
Language
English
Original Abstract
n this paper, we establish concentration and multiplicity properties of positive ground state solutions to the following perturbed pseudo-relativistic Schrödinger equation with competing potentials where N >2s, ϵ is a small positive parameter, and (−Δ+m2)s is the pseudo-relativistic Schrödinger operator with s∈(0,1) and mass m>0. We assume that the potentials V, K and the nonlinearity f are continuous but are not necessarily of class C1. Under natural hypotheses, combining the extension method, Nehari analysis and the Ljusternik-Schnirelmann category theory, we first study the existence and concentration phenomena of positive solutions for ϵ>0 sufficiently small, as well as multiplicity properties depending on the topology of the set where V attains its global minimum and K attains its global maximum. Moreover, we establish the asymptotic convergence and the exponential decay of positive solutions. In the final part of this paper, we provide a sufficient condition for the non-existence of ground state solutions.
Keywords
concentration; ground states; multiplicity; Pseudo-relativistic Schrödinger equation
Authors
RADULESCU, V.; ZHANG, W.; ZHANG, J.
Released
20. 3. 2025
ISBN
1539-6746
Periodical
Communications in Mathematical Sciences
Year of study
23
Number
2
State
United States of America
Pages from
465
Pages to
507
Pages count
43
URL
BibTex
@article{BUT197490,
author="Wen {Zhang} and Jian {Zhang} and Vicentiu {Radulescu}",
title="SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS",
journal="Communications in Mathematical Sciences",
year="2025",
volume="23",
number="2",
pages="465--507",
doi="10.4310/CMS.241217220205",
issn="1539-6746",
url="https://dx.doi.org/10.4310/CMS.241217220205"
}