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The Dirichlet Problem with Mean Curvature Operator in Minkowski Space – a Variational Approach

Abstract In this paper we consider the Dirichlet problem with mean curvature operator in Minkowski space : where Ω ⊂ ℝN is a smooth open bounded set and f : Ω × ℝ → ℝ is a Carathéodory function. We show that u is a solution of the above problem iff it is a critical point of the corresponding non-smooth action functional. Applications concerning nontrivial solutions for a class of such Dirichet problems depending on a parameter are provided.