Concentration and multiplicity of solutions for fractional double phase problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0197286" target="_blank" >RIV/00216305:26220/26:0197286 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/concentration-and-multiplicity-of-solutions-for-fractional-double-phase-problems/3C15C719D64358B5B7AC8E92A65E969B" target="_blank" >https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/concentration-and-multiplicity-of-solutions-for-fractional-double-phase-problems/3C15C719D64358B5B7AC8E92A65E969B</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/prm.2024.84" target="_blank" >10.1017/prm.2024.84</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Concentration and multiplicity of solutions for fractional double phase problems

Popis výsledku v původním jazyce

In the present paper, we consider the following fractional double phase problem with nonlo cal reaction: ( ( (-Delta)(p)(s)u + (-Delta)(q)(s) u + V (epsilon x)(|u|(p-2)u + |u|(q-2)u) = (1/|x|mu & lowast; F(u)f(u) in R-N, u is an element of W-s,W-p (R-N) boolean AND W-s,W-q(R-N), u > 0 in R-N } where epsilon is a positive parameter, 0 < s < 1, 2 p < q < min{2p, N/s }, 0 < <mu> < sp , (-Delta)(t)(s) (t is an element of { p, q }) is the fractional t-Laplace operator, the reaction term f : R 7 -> R is continuous, and the potential V is an element of C (R-N , R ) satisfying a local condition. Using a variational approach and topological tools (the non-standard C 1-Nehari manifold analysis and the abstract category theory), multiplicity of positive solutions and concentration properties for the above problem are established. Our results extend and complement some previous contributions related to double phase variational integrals.

Název v anglickém jazyce

Concentration and multiplicity of solutions for fractional double phase problems

Popis výsledku anglicky

In the present paper, we consider the following fractional double phase problem with nonlo cal reaction: ( ( (-Delta)(p)(s)u + (-Delta)(q)(s) u + V (epsilon x)(|u|(p-2)u + |u|(q-2)u) = (1/|x|mu & lowast; F(u)f(u) in R-N, u is an element of W-s,W-p (R-N) boolean AND W-s,W-q(R-N), u > 0 in R-N } where epsilon is a positive parameter, 0 < s < 1, 2 p < q < min{2p, N/s }, 0 < <mu> < sp , (-Delta)(t)(s) (t is an element of { p, q }) is the fractional t-Laplace operator, the reaction term f : R 7 -> R is continuous, and the potential V is an element of C (R-N , R ) satisfying a local condition. Using a variational approach and topological tools (the non-standard C 1-Nehari manifold analysis and the abstract category theory), multiplicity of positive solutions and concentration properties for the above problem are established. Our results extend and complement some previous contributions related to double phase variational integrals.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

ISSN

0308-2105

e-ISSN

1473-7124

Svazek periodika

2024

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

54

Strana od-do

1-54

Kód UT WoS článku

001364313900001

EID výsledku v databázi Scopus

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