SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Mathematical Sciences
ISSN
1539-6746
e-ISSN
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Volume of the periodical
23
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
43
Pages from-to
465-507
UT code for WoS article
001434061200006
EID of the result in the Scopus database
2-s2.0-85213986040