Ground states for quasilinear equations of N-Laplacian type with critical exponential growth and lack of compactness

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0198019" target="_blank" >RIV/00216305:26220/26:0198019 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11425-023-2298-1" target="_blank" >https://link.springer.com/article/10.1007/s11425-023-2298-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11425-023-2298-1" target="_blank" >10.1007/s11425-023-2298-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Ground states for quasilinear equations of N-Laplacian type with critical exponential growth and lack of compactness

Popis výsledku v původním jazyce

In this paper, (i) we present unified approaches to studying the existence of ground state solutions and mountain-pass type solutions for the following quasilinear equation: (Formula presented.) in three different cases allowing the potential V∈C(RN,R) to be periodic, radially symmetric, or asymptotically constant, where ΔNu:=div(∣∇u∣N−2∇u) and f has critical exponential growth; (ii) two new compactness lemmas in W1,N(ℝN) for general nonlinear functionals are established, which generalize the ones obtained in the radially symmetric space Wrad1,N(RN); (iii) based on some key observations, we construct a special path allowing us to control the mountain-pass minimax level by a fine threshold under which the compactness can be restored for the critical case. In particular, some delicate analyses are developed to overcome non-standard difficulties due to both the quasilinear characteristic of the equation and the lack of compactness aroused by the critical exponential growth of f. Our results extend and improve the ones of Alves et al. (2012), Ibrahim et al. (2015) (N = 2), and Masmoudi and Sani (2015) (N ⩾ 3) for the constant potential case, Alves and Figueiredo (2009) for the periodic potential case, Lam and Lu (2012) and Yang (2012) for the coercive potential case, and Chen et al. (Sci China Math, 2021) for the degenerate potential case, which are totally new even for the simpler semilinear case of N = 2. We believe that our approaches and strategies may be adapted and modified to attack more variational problems with critical exponential growth.

Název v anglickém jazyce

Ground states for quasilinear equations of N-Laplacian type with critical exponential growth and lack of compactness

Popis výsledku anglicky

In this paper, (i) we present unified approaches to studying the existence of ground state solutions and mountain-pass type solutions for the following quasilinear equation: (Formula presented.) in three different cases allowing the potential V∈C(RN,R) to be periodic, radially symmetric, or asymptotically constant, where ΔNu:=div(∣∇u∣N−2∇u) and f has critical exponential growth; (ii) two new compactness lemmas in W1,N(ℝN) for general nonlinear functionals are established, which generalize the ones obtained in the radially symmetric space Wrad1,N(RN); (iii) based on some key observations, we construct a special path allowing us to control the mountain-pass minimax level by a fine threshold under which the compactness can be restored for the critical case. In particular, some delicate analyses are developed to overcome non-standard difficulties due to both the quasilinear characteristic of the equation and the lack of compactness aroused by the critical exponential growth of f. Our results extend and improve the ones of Alves et al. (2012), Ibrahim et al. (2015) (N = 2), and Masmoudi and Sani (2015) (N ⩾ 3) for the constant potential case, Alves and Figueiredo (2009) for the periodic potential case, Lam and Lu (2012) and Yang (2012) for the coercive potential case, and Chen et al. (Sci China Math, 2021) for the degenerate potential case, which are totally new even for the simpler semilinear case of N = 2. We believe that our approaches and strategies may be adapted and modified to attack more variational problems with critical exponential growth.

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

2025

Kód důvěrnosti údajů

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

Název periodika

Science China. Mathematics

ISSN

1674-7283

e-ISSN

1869-1862

Svazek periodika

68

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CN - Čínská lidová republika

Počet stran výsledku

32

Strana od-do

1323-1354

Kód UT WoS článku

001362592100001

EID výsledku v databázi Scopus

2-s2.0-85204763135