On the behaviour of the solutions to p-laplacian equations as p goes to 1

被引：37
|
作者：
Mercaldo, A. [1 ]
Segura de Leon, S. [2 ]
Trombetti, C. [1 ]
机构：
[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy
[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain
来源：
PUBLICACIONS MATEMATIQUES | 2008年 / 52卷 / 02期
关键词：
nonlinear elliptic equations; 1-Laplace operator;
D O I：
10.5565/PUBLMAT_52208_07
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the present paper we study the behaviour as p goes to I of the weak solutions to the problems [GRAPHICS] where Omega is a bounded open set of R-N (N >= 2) with Lipschitz boundary and p > 1. As far as the datum f is concerned, we analyze several cases: the most general one is f epsilon W--1,W-infinity(Omega). We also illustrate our results by means of remarks and examples.
引用
收藏
页码：377 / 411
页数：35
相关论文
共 50 条
  • [41] Existence of periodic solutions for a class of p-Laplacian equations
    Chang, Xiaojun
    Qiao, Yu
    BOUNDARY VALUE PROBLEMS, 2013,
  • [42] Existence of solutions for perturbed fractional p-Laplacian equations
    Xiang, Mingqi
    Zhang, Binlin
    Radulescu, Vicentiu D.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (02) : 1392 - 1413
  • [43] Existence and multiplicity of solutions to p-Laplacian equations on graphs
    Shao, Mengqiu
    REVISTA MATEMATICA COMPLUTENSE, 2024, 37 (01): : 185 - 203
  • [44] Positive solutions of nonlinear p-Laplacian equations in Rn
    Liu, HH
    Su, N
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 317 (01) : 207 - 227
  • [45] Solutions to equations of p-Laplacian type in Lorentz spaces
    De Nápoli, P
    Mariani, MC
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2001, 8 (03) : 469 - 477
  • [46] Existence of solutions for asymptotically 'linear' p-Laplacian equations
    Liu, S
    Li, S
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 : 81 - 87
  • [47] Periodic solutions for p-Laplacian Rayleigh equations with singularities
    Shipin Lu
    Tao Zhong
    Lijuan Chen
    Boundary Value Problems, 2016
  • [48] Existence and multiplicity of solutions for a class of p-Laplacian equations
    Li, Lin
    Chen, Shang-Jie
    APPLIED MATHEMATICS LETTERS, 2014, 27 : 59 - 63
  • [49] On the existence of positive solutions of p-Laplacian difference equations
    He, ZM
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 161 (01) : 193 - 201
  • [50] EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR p-LAPLACIAN EQUATIONS
    Gao, Ting-Mei
    Tang, Chun-Lei
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
12345