Detail publikace

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

CHEN, S. QIN, D. RADULESCU, V. TANG, X.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

critical exponential growth; ground state solution; N-Laplacian equations; Nehari manifold; Trudinger-Moser inequality

Autoři

CHEN, S.; QIN, D.; RADULESCU, V.; TANG, X.

Vydáno

2. 6. 2025

ISSN

1869-1862

Periodikum

Science China-Mathematics

Ročník

68

Číslo

6

Stát

Čínská lidová republika

Strany od

1323

Strany do

1354

Strany počet

32

URL

https://link.springer.com/article/10.1007/s11425-023-2298-1

BibTex

@article{BUT198019,
  author="Sitong {Chen} and Dongdong {Qin} and Vicentiu {Radulescu} and Xianhua {Tang}",
  title="Ground states for quasilinear equations of N-Laplacian type with critical exponential growth and lack of compactness",
  journal="Science China-Mathematics",
  year="2025",
  volume="68",
  number="6",
  pages="1323--1354",
  doi="10.1007/s11425-023-2298-1",
  issn="1869-1862",
  url="https://link.springer.com/article/10.1007/s11425-023-2298-1"
}