EXISTENCE OF WEAK SOLUTIONS FOR A SEMILINEAR PROBLEM WITH A NONLINEAR BOUNDARY CONDITION

被引：0

作者：

Afrouzi, G. A. ^{[1
]}

Mirzapour, M. ^{[1
]}

Hadjian, A. ^{[1
]}

Shakeri, S. ^{[1
]}

机构：

[1] Univ Mazan Daran, Fac Math Sci, Dept Math, Babol Sar, Iran

来源：

BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 3卷 / 03期

关键词：

Semilinear elliptic equation; Nonlinear boundary condition; Landesman-Lazer type conditions; Minimum principle;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper shows conditions for the existence of weak solutions of the problem {-Delta u = lambda(1)u + f(x, u) - h (x) in Omega, partial derivative u/partial derivative n = g(x, u) on partial derivative Omega, where Omega is a bounded domain in R-N (N >= 1) with smooth boundary, partial derivative u/partial derivative n denotes the derivative of u with respect to the outer normal n, f : Omega x R -> R and g : partial derivative Omega x R -> R are bounded Caratheodory functions, h is an element of L-2 ( Omega) and lambda(1) > 0 is the principal eigenvalue of -Delta on Omega with zero Dirichlet boundary conditions. Our method is based on the minimum principle.

引用

页码：109 / 114

页数：6

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