ZERO ORDER PERTURBATIONS TO FULLY NONLINEAR EQUATIONS: COMPARISON, EXISTENCE AND UNIQUENESS

被引：13

作者：

Charro, Fernando ^{[1
]}

Peral, Ireneo ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2009年 / 11卷 / 01期

关键词：

Elliptic equations; fully nonlinear; comparison principles; viscosity solutions; existence; uniqueness; STRONG MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; DIRICHLET PROBLEM; ELLIPTIC-EQUATIONS; INFINITY; EIGENVALUE;

D O I：

10.1142/S0219199709003296

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study existence of solutions to {F(del u, D(2)u) = f(lambda, u) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where F is elliptic and homogeneous of degree m, and either f(lambda, u) = lambda u(q) or f(lambda, u) = lambda u(q) + u(r), for 0 < q < m < r, and lambda > 0. Furthermore, in the first case, we obtain that the solution is unique as a consequence of a comparison principle up to the boundary. Several examples, including uniformly elliptic operators and the infinity-laplacian, are considered.

引用

页码：131 / 164

页数：34

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