Existence of positive solutions for nonlinear elliptic equations with convection terms

被引：8

作者：

Motreanu, D. ^{[1
]}

Tanaka, M. ^{[2
]}

机构：

[1] Univ Perpignan, Dept Math, F-66860 Perpignan, France

[2] Tokyo Univ Sci, Dept Math, Shinjyuku Ku, Kagurazaka 1-3, Tokyo 1628601, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 152卷

关键词：

Nonlinear elliptic equation; Convection term; Strong maximum principle; STRONG MAXIMUM PRINCIPLE; DEPENDENCE; GRADIENT;

D O I：

10.1016/j.na.2016.12.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of positive solutions for the equation -Sigma(N)(i=1) partial derivative/partial derivative x(i)ai(x, u, del u) = f (x, u, del u) in Omega under the Dirichlet boundary condition, where the essential point is the dependence of the terms of the elliptic equation on the solution u and its gradient del u. We develop an approach based on approximate solutions and on a new strong maximum principle. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：38 / 60

页数：23

共 50 条

[1] Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus
Gou, Haide
[J]. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2023, 9 (02) : 807 - 829
[2] Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus
Haide Gou
[J]. Journal of Elliptic and Parabolic Equations, 2023, 9 : 807 - 829
[3] On the existence of positive solutions of nonlinear elliptic equations
Mâatoug, L
Masmoudi, S
[J]. POTENTIAL ANALYSIS, 2001, 15 (03) : 187 - 197
[4] On the Existence of Positive Solutions of Nonlinear Elliptic Equations
L. M^aatoug
S. Masmoudi
[J]. Potential Analysis, 2001, 15 : 187 - 197
[5] Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
Li, Yongxiang
Ma, Weifeng
[J]. ENTROPY, 2022, 24 (12)
[6] EXISTENCE OF TWO POSITIVE SOLUTIONS FOR ANISOTROPIC NONLINEAR ELLIPTIC EQUATIONS
Bonanno, G.
D'Agui, G.
Sciammetta, A.
[J]. ADVANCES IN DIFFERENTIAL EQUATIONS, 2021, 26 (5-6) : 229 - 258
[7] Existence of positive entire solutions of fully nonlinear elliptic equations
Vitolo A.
[J]. Journal of Elliptic and Parabolic Equations, 2018, 4 (2) : 293 - 304
[8] EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR FRACTIONAL NEUMANN ELLIPTIC EQUATIONS
Ni, Haige
Xia, Aliang
Zheng, Xiongjun
[J]. DIFFERENTIAL EQUATIONS & APPLICATIONS, 2018, 10 (01): : 115 - 129
[9] EXISTENCE OF SOLUTIONS TO SINGULAR ELLIPTIC EQUATIONS WITH CONVECTION TERMS VIA THE GALERKIN METHOD
Alves, Claudianor O.
Carriao, Paulo C.
Faria, Luiz F. O.
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010,
[10] Positive radial solutions for elliptic equations with nonlinear gradient terms in an annulus
Li, Yongxiang
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2018, 63 (02) : 171 - 187

← 1 2 3 4 5 →