Existence and multiplicity of positive solutions of a one-dimensional mean curvature equation in Minkowski space

Abstract

Abstract In this paper, we consider a one-dimensional mean curvature equation in Minkowski space and the corresponding one-parameter problem. By using a fixed point theorem of cone expansion and compression of norm type, the existence and multiplicity of positive solutions for the above problems are obtained. Meanwhile, as applications of our results, some examples are given.

Keywords

• Mean curvature equations
• Positive solution
• Existence
• Multiplicity
• Fixed point theorem of cone expansion and compression of norm type