Necessary and sufficient conditions for the existence of nonnegative solutions of inhomogeneous p-Laplace equation

被引：8

作者：

Dai Qiuyi ^{[1
]}

Peng Lihui

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310028, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2007年 / 27卷 / 01期

基金：

中国国家自然科学基金;

关键词：

inhomogeneous p-Laplace equation; Dirichlet problem; nonnegative solution; SEMILINEAR ELLIPTIC-EQUATIONS; MULTIPLE POSITIVE SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; CRITICAL-POINT THEORY; NONEXISTENCE; REGULARITY; EXPONENT;

D O I：

10.1016/S0252-9602(07)60004-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Omega be a smooth bounded domain in R-n. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -Delta(p)u = \u\(q-1)u + lambda f (x) on Omega, and identify necessary and sufficient conditions on Omega and f (x) which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

引用

页码：34 / 56

页数：23

共 50 条

[31] Stability for p-Laplace type equation in a borderline case
Farroni, Fernando
Greco, Luigi
Moscariello, Gioconda
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 116 : 100 - 111
[32] On a Class of Weighted p-Laplace Equation with Singular Nonlinearity
Garain, Prashanta
Mukherjee, Tuhina
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2020, 17 (04)
[33] Some notes on supersolutions of fractional p-Laplace equation
Shi, Shaoguang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 463 (02) : 1052 - 1074
[34] Gradient estimates for the p-laplace equation with a singular source
Dias, Gilberlandio J.
Duarte, italo B. M.
JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2024, 10 (02) : 899 - 914
[35] Classification of positive D1,p(RN)-solutions to the critical p-Laplace equation in RN
Sciunzi, Berardino
ADVANCES IN MATHEMATICS, 2016, 291 : 12 - 23
[36] Existence and uniqueness for p-Laplace equations involving singular nonlinearities
Canino, Annamaria
Sciunzi, Berardino
Trombetta, Alessandro
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2016, 23 (02):
[37] A necessary and sufficient condition for the existence of entire large solutions to a k-Hessian system
Zhang, Xinguang
Chen, Peng
Wu, Yonghong
Wiwatanapataphee, Benchawan
APPLIED MATHEMATICS LETTERS, 2023, 145
[38] A NECESSARY AND A SUFFICIENT CONDITION FOR THE EXISTENCE OF THE POSITIVE RADIAL SOLUTIONS TO HESSIAN EQUATIONS AND SYSTEMS WITH WEIGHTS
Covei, Dragos-Patru
ACTA MATHEMATICA SCIENTIA, 2017, 37 (01) : 47 - 57
[39] Uniqueness of bounded solutions to p-Laplace problems in strips
Phuong Le
COMPTES RENDUS MATHEMATIQUE, 2023, 361 (01) : 795 - 801
[40] Multiple solutions for the p-Laplace operator with critical growth
De Napoli, Pablo L.
Fernandez Bonder, Julian
Silva, Analia
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : 6283 - 6289

← 1 2 3 4 5 →