On the existence of positive solutions of nonlinear elliptic equations

被引：0

作者：

Mâatoug, L ^{[1
]}

Masmoudi, S ^{[1
]}

机构：

[1] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

POTENTIAL ANALYSIS | 2001年 / 15卷 / 03期

关键词：

Kato's measure; additive functional; Green's function; Schauder's fixed point theorem; nonlinear elliptic problem; positive solution;

D O I：

10.1023/A:1011226603618

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of positive solutions of the nonlinear elliptic problem 1/2 Deltau - f(u) . mu + g(u) . sigma = 0 in D with u = 0 on partial derivativeD, where mu and sigma are two Randon's measures belonging to a Kato subclass and D is an unbounded smouth domain in R-d(d greater than or equal to 3). When g is superlinear at 0 and 0 less than or equal to f(t) less than or equal to t for t is an element of (0,b), then probabilistic methods and fixed point argument are used to prove the existence of infinitely many bounded continuous solutions of this problem.

引用

页码：187 / 197

页数：11

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