Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151072" target="_blank" >RIV/00216305:26220/24:PU151072 - isvavai.cz</a>

Výsledek na webu

<a href="https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0022039624000536?via%3Dihub" target="_blank" >https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0022039624000536?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2024.01.041" target="_blank" >10.1016/j.jde.2024.01.041</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth

Popis výsledku v původním jazyce

In this paper, we study the following (p,q)-Laplacian equation with Lp-constraint: {−Δpu−Δqu+λ|u|p−2u=f(u),inRN,∫R|u|pdx=cp,u∈W1,p(RN)∩W1,q(RN), where 1<p<q<N, Δi=div(|∇u|i−2∇u), with i∈{p,q}, is the i-Laplacian operator, λ is a Lagrange multiplier and c>0 is a constant. The nonlinearity f is assumed to be continuous and satisfying weak mass supercritical conditions. The purpose of this paper is twofold: to establish the existence of ground states, and to reveal the basic behavior of the ground state energy Ec as c>0 varies. Moreover, we introduce a new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball of radius cp in Lp(RN). The analysis developed in this paper allows to provide the general growth assumptions imposed to the reaction f.

Název v anglickém jazyce

Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth

Popis výsledku anglicky

In this paper, we study the following (p,q)-Laplacian equation with Lp-constraint: {−Δpu−Δqu+λ|u|p−2u=f(u),inRN,∫R|u|pdx=cp,u∈W1,p(RN)∩W1,q(RN), where 1<p<q<N, Δi=div(|∇u|i−2∇u), with i∈{p,q}, is the i-Laplacian operator, λ is a Lagrange multiplier and c>0 is a constant. The nonlinearity f is assumed to be continuous and satisfying weak mass supercritical conditions. The purpose of this paper is twofold: to establish the existence of ground states, and to reveal the basic behavior of the ground state energy Ec as c>0 varies. Moreover, we introduce a new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball of radius cp in Lp(RN). The analysis developed in this paper allows to provide the general growth assumptions imposed to the reaction f.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure 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

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

391

Číslo periodika v rámci svazku

2024

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

48

Strana od-do

57-104

Kód UT WoS článku

001183392300001

EID výsledku v databázi Scopus

2-s2.0-85183953232