Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0201755" target="_blank" >RIV/00216305:26220/26:0201755 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s13324-026-01182-x?utm_source=getftr&utm_medium=getftr&utm_campaign=getftr_pilot&getft_integrator=clarivate" target="_blank" >https://link.springer.com/article/10.1007/s13324-026-01182-x?utm_source=getftr&utm_medium=getftr&utm_campaign=getftr_pilot&getft_integrator=clarivate</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13324-026-01182-x" target="_blank" >10.1007/s13324-026-01182-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction

Popis výsledku v původním jazyce

This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction {-epsilon(p)Delta(p)u - epsilon(q)Delta(q)u + V(x)(|u|(p-2)u + |u|(q-2)u) = epsilon(& micro;-N) ( 1 / |x|(& micro;) * G(u)) g(u), in R-N, u is an element of W-1,W-p(R-N) boolean AND W-1,W-q(R-N), u > 0, in R-N, where 1 < p < q < N, 0 < & micro; < p, epsilon is a small positive parameter and V is the absorption potential. We assume that the potential V satisfies only a local condition introduced by del Pino and Felmer. Applying suitable variational and topological methods combined with penalization technique, we obtain multiple semiclassical positive solutions for epsilon > 0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum. Moreover, we also investigate the decay property of semiclassical positive solutions. The main results included in this paper complement several recent contributions to the study of concentration phenomena.

Název v anglickém jazyce

Localized concentration of semiclassical solutions for double phase problems with nonlocal reaction

Popis výsledku anglicky

This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction {-epsilon(p)Delta(p)u - epsilon(q)Delta(q)u + V(x)(|u|(p-2)u + |u|(q-2)u) = epsilon(& micro;-N) ( 1 / |x|(& micro;) * G(u)) g(u), in R-N, u is an element of W-1,W-p(R-N) boolean AND W-1,W-q(R-N), u > 0, in R-N, where 1 < p < q < N, 0 < & micro; < p, epsilon is a small positive parameter and V is the absorption potential. We assume that the potential V satisfies only a local condition introduced by del Pino and Felmer. Applying suitable variational and topological methods combined with penalization technique, we obtain multiple semiclassical positive solutions for epsilon > 0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum. Moreover, we also investigate the decay property of semiclassical positive solutions. The main results included in this paper complement several recent contributions to the study of concentration phenomena.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2026

Kód důvěrnosti údajů

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

Název periodika

Analysis and mathematical physics

ISSN

1664-2368

e-ISSN

1664-235X

Svazek periodika

16

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

54

Strana od-do

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Kód UT WoS článku

001717080000001

EID výsledku v databázi Scopus

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