Nontrivial Solutions for Potential Systems Involving the Mean Curvature Operator in Minkowski Space

Abstract

In this paper, we use the critical point theory for convex, lower semicontinuous perturbations of C1{C^{1}}-functionals to obtain the existence of multiple nontrivial solutions for one parameter potential systems involving the operator u↦div⁡(∇⁡u1-|∇⁡u|2){u\mapsto\operatorname{div}(\frac{\nabla u}{\sqrt{1-|\nabla u|^{2}}})}. The solvability of a general non-potential system is also established.

Keywords

• minkowski operator
• potential system
• multiple nontrivial solutions
• critical point
• mountain pass theorem
• schauder’s fixed point theorem
• 35b38
• 35j50
• 49j40