Estimates on the Green function and existence of positive solutions for some nonlinear polyharmonic problems outside the unit ball

被引：5

作者：

Bachar, Imed ^{[1
]}

Maagli, Habib ^{[1
]}

Zeddini, Noureddine ^{[1
]}

机构：

[1] Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia

来源：

ANALYSIS AND APPLICATIONS | 2008年 / 6卷 / 02期

关键词：

Green's function; Kato's class; positive solution; Schauder fixed point theorem; polyharmonic elliptic equation;

D O I：

10.1142/S0219530508001092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G(m,n)(D) be the Green function of (-Delta)(m), m >= 1, on the complementary D of the unit closed ball in R-n, n >= 2, with Dirichlet boundary conditions (partial derivative/partial derivative nu)(j) =0, 0 <= j <= m-1. We establish some estimates on G(m,n)(D) including the 3G- Inequality given by (1.3). Next, we introduce a polyharmonic Kato class of functions K-m,n(infinity)(D) and we exploit the properties of this class to study the existence of positive solutions of some polyharmonic nonlinear elliptic problems.

引用

页码：121 / 150

页数：30

共 22 条

[1]

[Anonymous], SIAM CLASSICS APPL M

[2] On a singular semilinear elliptic boundary value problem and the boundary Harnack principle [J].