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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2026

Confidentiality

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

Name of the periodical

Analysis and mathematical physics

ISSN

1664-2368

e-ISSN

1664-235X

Volume of the periodical

16

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

54

Pages from-to

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UT code for WoS article

001717080000001

EID of the result in the Scopus database

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