SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F25%3APU156152" target="_blank" >RIV/00216305:26220/25:PU156152 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.4310/CMS.241217220205" target="_blank" >https://dx.doi.org/10.4310/CMS.241217220205</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4310/CMS.241217220205" target="_blank" >10.4310/CMS.241217220205</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematical Sciences

ISSN

1539-6746

e-ISSN

—

Svazek periodika

23

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

465-507

Kód UT WoS článku

001434061200006

EID výsledku v databázi Scopus

2-s2.0-85213986040