QUASILINEAR SCHRODINGER EQUATIONS WITH SINGULAR AND VANISHING POTENTIALS INVOLVING NONLINEARITIES WITH CRITICAL EXPONENTIAL GROWTH

被引：5
|
作者：
Araujo, Yane Lisley [1 ]
Carvalho, Gilson [1 ]
Clemente, Rodrigo [1 ]
机构：
[1] Univ Fed Rural Pernambuco, Dept Math, BR-52171900 Recife, PE, Brazil
来源：
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2021年 / 57卷 / 01期
关键词：
Variational methods; critical exponential growth; Schodinger equation; unbounded or decaying potentials; ELLIPTIC-EQUATIONS; EXISTENCE; COMPACTNESS; SPACES;
D O I：
10.12775/TMNA.2020.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the following class of Schrodinger equations: -Delta(N)u+ V(vertical bar x vertical bar))vertical bar u vertical bar(N-2)u = Q(vertical bar x vertical bar h(u) in R-N, where N >= 2, V, Q: R-N -> R are potentials that can be unbounded, decaying or vanishing at infinity and the nonlinearity h: R -> R has a critical exponential growth concerning the Trudinger Moser inequality. By using a variational approach, a version of the Trudinger Moser inequality and a symmetric criticality type result, we obtain the existence of nonnegative weak and ground state solutions for this class of problems and under suitable assumptions, we obtain a nonexistence result.
引用
收藏
页码：317 / 342
页数：26
相关论文
共 50 条
  • [41] Existence and multiplicity results for a class of quasilinear Schrodinger equations in RN involving critical growth
    Song, Yueqiang
    Shi, Shaoyun
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017, 62 (07) : 967 - 1001
  • [42] Solutions for Singular Quasilinear Equations of N-Laplacian Type with Critical Exponential Growth
    Liu, Boxue
    Lai, Lizhen
    Qin, Dongdong
    Sahara, Siti
    Wu, Qingfang
    JOURNAL OF GEOMETRIC ANALYSIS, 2024, 34 (11)
  • [43] Multiple solutions for quasilinear Schrodinger equations involving critical exponent
    Wang Youjun
    Zhang Yimin
    Shen Yaotian
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (03) : 849 - 856
  • [44] Modified quasilinear equations with strongly singular and critical exponential nonlinearity
    Biswas, Reshmi
    Goyal, Sarika
    Sreenadh, Konijeti
    ADVANCES IN NONLINEAR ANALYSIS, 2024, 13 (01)
  • [45] Quasilinear elliptic equations involving the N-Laplacian with critical exponential growth in RN
    Wang, Youjun
    Yang, Jun
    Zhang, Yimin
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : 6157 - 6169
  • [46] Quasilinear Schrodinger equations with a positive parameter and involving unbounded or decaying potentials
    Severo, Uberlandio B.
    de Carvalho, Gilson M.
    APPLICABLE ANALYSIS, 2021, 100 (02) : 229 - 252
  • [47] Solutions for a class of singular quasilinear equations involving critical growth in R2
    de Souza, Manasses X.
    Severo, Uberlandio B.
    Vieira, Gilberto F.
    MATHEMATISCHE NACHRICHTEN, 2022, 295 (01) : 103 - 123
  • [48] QUASILINEAR NONHOMOGENEOUS SCHRODINGER EQUATION WITH CRITICAL EXPONENTIAL GROWTH IN Rn
    de Souza, Manasses
    do O, Joao Marcos
    Silva, Tarciana
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2015, 45 (02) : 615 - 639
  • [49] Critical quasilinear equations with singular potentials via perturbation method
    Yu Su
    Hongxia Shi
    Monatshefte für Mathematik, 2022, 199 : 627 - 644
  • [50] Critical quasilinear equations with singular potentials via perturbation method
    Su, Yu
    Shi, Hongxia
    MONATSHEFTE FUR MATHEMATIK, 2022, 199 (03): : 627 - 644
12345