Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU149856" target="_blank" >RIV/00216305:26220/24:PU149856 - isvavai.cz</a>

Výsledek na webu

<a href="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001089369200001" target="_blank" >https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001089369200001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/forum-2023-0183" target="_blank" >10.1515/forum-2023-0183</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

Popis výsledku v původním jazyce

This paper is concerned with the following fractional (N/s)-Laplacian Choquard equation: epsilon(N )(-Delta)(s)(N/s)u + V(x)|u|(N/s-2)u = epsilon(mu)(1 / |x|(N-mu )& lowast;F(u) )f(u), x is an element of R-N,where (-Delta)(s)(N/s) denotes the (N/s)-Laplacian operator, 0 < mu < N, and V and f are continuous real functions satisfying some mild assumptions. Applying the weak growth conditions on the exponential critical nonlinearity f and without using the strictly monotone condition, we use some refined analysis and develop the arguments in the existing results to establish the existence of the ground state solution of the fractional (N/s)-Laplacian Choquard equation. Moreover, we also study the concentration phenomenon of the ground state solutions. As far as we know, our results seem to be new concerning the fractional (N/s)-Laplacian equation with the Choquard reaction.

Název v anglickém jazyce

Concentrating solutions for singularly perturbed fractional (N/s)-Laplacian equations with nonlocal reaction

Popis výsledku anglicky

This paper is concerned with the following fractional (N/s)-Laplacian Choquard equation: epsilon(N )(-Delta)(s)(N/s)u + V(x)|u|(N/s-2)u = epsilon(mu)(1 / |x|(N-mu )& lowast;F(u) )f(u), x is an element of R-N,where (-Delta)(s)(N/s) denotes the (N/s)-Laplacian operator, 0 < mu < N, and V and f are continuous real functions satisfying some mild assumptions. Applying the weak growth conditions on the exponential critical nonlinearity f and without using the strictly monotone condition, we use some refined analysis and develop the arguments in the existing results to establish the existence of the ground state solution of the fractional (N/s)-Laplacian Choquard equation. Moreover, we also study the concentration phenomenon of the ground state solutions. As far as we know, our results seem to be new concerning the fractional (N/s)-Laplacian equation with the Choquard reaction.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

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

FORUM MATHEMATICUM

ISSN

0933-7741

e-ISSN

1435-5337

Svazek periodika

36

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

28

Strana od-do

783-810

Kód UT WoS článku

001089369200001

EID výsledku v databázi Scopus

2-s2.0-85176213182