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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

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

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

Science China. Mathematics

ISSN

1674-7283

e-ISSN

1869-1862

Volume of the periodical

68

Issue of the periodical within the volume

6

Country of publishing house

CN - CHINA

Number of pages

32

Pages from-to

1323-1354

UT code for WoS article

001362592100001

EID of the result in the Scopus database

2-s2.0-85204763135