Denumerably many positive radial solutions for the iterative system of Minkowski-Curvature equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Dr. Lankapalli Bullayya College, Resapuvanipalem, Visakhapatnam, 530013, India

2 Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003, India

3 Department of Mathematics, College of Engineering for Women, Gayatri Vidya Parishad, Madhurawada, Visakhapatnam, 530048, India

Abstract

This paper deals with the existence of denumerably many positive radial solutions to the iterative system of Dirichlet problems
$$
div(\frac{\nabla z_j}{\sqrt{1-|\nabla z_j|^2}})+g_j(z_{j+1})=0\ in\ \Omega,$$
$$z_j=0\ on\ \partial\Omega,$$
where $j\in\{1, 2,\cdot\cdot\cdot,n\},$ $z_1=z_{n+1},$ $\Omega$ is a unit ball in $\mathbb{R}^N$ involving the mean curvature operator in Minkowski space by applying Krasnoselskii's fixed point theorem, Avery-Henderson fixed point theorem and a new (Ren-Ge-Ren) fixed point theorem in cones.

Keywords