Existence of multiple radial solutions for nonlinear equation involving the mean curvature operator in Lorentz-Minkowski space

TL;DR

This paper establishes the existence of multiple radial solutions for nonlinear mean curvature equations in Lorentz-Minkowski space using critical point theory, expanding understanding of solution multiplicity in geometric PDEs.

Contribution

It introduces new multiplicity results for nonlinear mean curvature equations in Lorentz-Minkowski space, employing non-smooth critical point theory and considering gradient-dependent nonlinearities.

Findings

Multiple radial solutions are proven to exist.

Solutions are obtained via Szulkin's critical point theory.

Results include cases with gradient-dependent nonlinearities.

Abstract

We prove existence of multiple radial solutions to the Dirichlet problem for nonlinear equations involving the mean curvature operator in Lorentz-Minkowski space and a nonlinear term of concave-convex type. Solutions are found using Szulkin's critical point theory for non-smooth functional. Multiplicity results are also given for some cases in which the nonlinearity depends also on the gradient of the solution.