Existence results for Dirichlet problems about two mean curvature equations in Euclidean and Minkowski spaces

Abstract

Let $$H_L$$ and $$H_R$$ be the extrinsic mean curvatures of a spacelike graph in Minkowski space $$\mathbb {L}^{N+1}$$ and Euclidean space $$\mathbb {R}^{N+1}$$ , respectively. In this paper, we establish the existence of multiple positive radial solutions for the Dirichlet problem of two nonlinear partial differential equations involving $$H_L$$ and $$H_R$$ .