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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Corsato, Chiara¹  Obersnel, Franco¹  Omari, Pierpaolo¹  Rivetti, Sabrina¹ 

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

关键词: Mean curvature;    Minkowski space;    Quasilinear elliptic equation;    Dirichlet boundary condition;    Positive solution;    Existence;    Multiplicity;    Non-existence;    Topological degree;    Critical point theory;   

DOI  :  10.1016/j.jmaa.2013.04.003

来源: Elsevier

【 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.

【 授权许可】

Free