user

A 1-Laplacian equation with critical and discontinuous nonlinearities

被引：0
|
作者：
Pimenta, Marcos Tadeu de Oliveira [1 ]
dos Santos Junior, Joao R. [2 ]
Stapenhorst, Matheus F. [1 ]
机构：
[1] Univ Estadual Paulista Unesp, Dept Matemat & Computacao, BR-19060900 Presidente Prudente, SP, Brazil
[2] Univ Fed, Fac Matemat, BR-66075110 Belem, Brazil
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 402卷
基金：
巴西圣保罗研究基金会;
关键词：
1-Laplacian operator; Discontinuous nonlinearities; Critical growth; DIFFERENTIAL-EQUATIONS; MULTIPLE SOLUTIONS; ELLIPTIC PROBLEMS;
D O I：
10.1016/j.jde.2024.05.014
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity with a critical Sobolev growth is studied. Through an argument based on an approximation method, an existence result is proved. In order to overcome the lack of compactness, we apply the well known concentration-compactness technique. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
引用
收藏
页码：463 / 494
页数：32
相关论文
共 50 条
  • [1] Bounded solutions to the 1-Laplacian equation with a critical gradient term
    Andreu, Fuensanta
    Dall'Aglio, Andrea
    de Leon, Sergio Segura
    [J]. ASYMPTOTIC ANALYSIS, 2012, 80 (1-2) : 21 - 43
  • [2] Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
    Carranza, Yino B. Cueva
    Pimenta, Marcos T. O.
    [J]. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2024, 73 (03) : 1037 - 1058
  • [3] Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities
    Yino B. Cueva Carranza
    Marcos T. O. Pimenta
    [J]. Rendiconti del Circolo Matematico di Palermo Series 2, 2024, 73 : 1037 - 1058
  • [4] N-Laplacian critical problem with discontinuous nonlinearities
    Tiwari, Sweta
    [J]. ADVANCES IN NONLINEAR ANALYSIS, 2015, 4 (02) : 109 - 121
  • [5] On the solutions to 1-Laplacian equation with L1 data
    Mercaldo, A.
    de Leon, S. Segura
    Trombetti, C.
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (08) : 2387 - 2416
  • [6] 1-Laplacian type problems with strongly singular nonlinearities and gradient terms
    Giachetti, Daniela
    Oliva, Francescantonio
    Petitta, Francesco
    [J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 24 (10)
  • [7] On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
    Pimenta, Marcos T. O.
    dos Santos, Gelson Conceicao G.
    Santos Junior, Joao R.
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2024, 154 (01) : 33 - 59
  • [8] On a fractional (p,q)-Laplacian equation with critical nonlinearities
    Shen, Yansheng
    [J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2024,
  • [9] THE 1-LAPLACIAN ELLIPTIC EQUATION WITH INHOMOGENEOUS ROBIN BOUNDARY CONDITIONS
    Mazon, Jose M.
    Rossi, Julio D.
    Segura de Leon, Sergio
    [J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2015, 28 (5-6) : 409 - 430
  • [10] ON THE SOLUTIONS OF NONLOCAL 1-LAPLACIAN EQUATION WITH L1-DATA
    Li, Dingding
    Zhang, Chao
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2024, 44 (05) : 1354 - 1375
12345