Quasilinear equation with critical exponential growth in the zero mass case

被引：2
作者：
de Albuquerque, J. C. [1 ]
Carvalho, J. [2 ]
机构：
[1] Univ Fed Pernambuco, Dept Matemat, BR-50670901 Recife, PE, Brazil
[2] Univ Fed Sergipe, Dept Matemat, BR-49100000 Sao Cristovao, SE, Brazil
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 232卷
关键词：
Zero-mass case; Hardy inequality; Weighted Sobolev embedding; Trudinger-Moser inequality; NONLINEAR SCHRODINGER-EQUATIONS; ELLIPTIC EIGENVALUE PROBLEMS; EXISTENCE; INEQUALITIES; POTENTIALS; R(N);
D O I：
10.1016/j.na.2023.113286
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work we study the existence of solutions for the following class of quasilinear elliptic equations -div (A(|x|)| backward difference u|N-2 backward difference u) = Q(|x|)f(u), in RN, where N & GE; 2 and f has critical exponential growth. We establish conditions on the non-homogeneous weights A and Q to introduce a suitable function space where we are able to apply Variational Methods to obtain weak solutions. The main key is a Hardy type inequality for radial functions. Our approach is based on a new Trudinger-Moser type inequality, a version of the Symmetric Criticality Principle and Mountain Pass Theorem. & COPY; 2023 Elsevier Ltd. All rights reserved.
引用
收藏
页数：19
相关论文
共 38 条
  • [1] Trudinger type inequalities in RN and their best exponents
    Adachi, S
    Tanaka, K
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (07) : 2051 - 2057
  • [2] Albuquerque FSB, 2021, MILAN J MATH, V89, P263, DOI 10.1007/s00032-021-00334-x
  • [3] Nonlinear Schrodinger equation with unbounded or decaying radial potentials involving exponential critical growth in R2
    Albuquerque, Francisco S. B.
    Alves, Claudianor O.
    Medeiros, Everaldo S.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (02) : 1021 - 1031
  • [4] Existence of solutions for a class of nonlinear Schrodinger equations with potential vanishing at infinity
    Alves, Claudianor O.
    Souto, Marco A. S.
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (04) : 1977 - 1991
  • [5] Aouaoui S, 2019, ANN MAT PUR APPL, V198, P1331, DOI 10.1007/s10231-018-00821-w
  • [6] QUASILINEAR SCHRODINGER EQUATIONS WITH SINGULAR AND VANISHING POTENTIALS INVOLVING NONLINEARITIES WITH CRITICAL EXPONENTIAL GROWTH
    Araujo, Yane Lisley
    Carvalho, Gilson
    Clemente, Rodrigo
    [J]. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2021, 57 (01) : 317 - 342
  • [7] Autuori G, 2013, ADV DIFFERENTIAL EQU, V18, P1
  • [8] Compactness and existence results for quasilinear elliptic problems with singular or vanishing potentials
    Badiale, Marino
    Guida, Michela
    Rolando, Sergio
    [J]. ANALYSIS AND APPLICATIONS, 2021, 19 (05) : 751 - 777
  • [9] Radial Nonlinear Elliptic Problems with Singular or Vanishing Potentials
    Badiale, Marino
    Zaccagni, Federica
    [J]. ADVANCED NONLINEAR STUDIES, 2018, 18 (02) : 409 - 428
  • [10] Sum of weighted Lebesgue spaces and nonlinear elliptic equations
    Badiale, Marino
    Pisani, Lorenzo
    Rolando, Sergio
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2011, 18 (04): : 369 - 405
1234