Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space

被引：85

作者：

Corsato, Chiara ^{[1
]}

Obersnel, Franco ^{[1
]}

Omari, Pierpaolo ^{[1
]}

Rivetti, Sabrina ^{[1
]}

机构：

[1] Univ Trieste, Dipartimento Matemat & Geosci, I-34127 Trieste, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 405卷 / 01期

关键词：

Mean curvature; Minkowski space; Quasilinear elliptic equation; Dirichlet boundary condition; Positive solution; Existence; Multiplicity; Non-existence; Topological degree; Critical point theory; LOCAL SUPERLINEARITY; HYPERSURFACES; SUBLINEARITY;

D O I：

10.1016/j.jmaa.2013.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space {-div(del u/root 1-vertical bar del u vertical bar(2)) = f(x, u, del u) in Omega, u = 0 on partial derivative Omega. Here Omega is a bounded regular domain in R-N and the function f = f(x, s, xi) is either sublinear, or superlinear, or sub-superlinear near s = 0. The proof combines topological and variational methods. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：227 / 239

页数：13

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