Minimax Inequality for a Special Class of Functionals and its Application for Elliptic Equations Involving the pLaplacian with Dirichlet Boundary Condition

In this paper, we establish an equivalent statement of minimax inequality for a special class of functionals. As an application, a result for the Dirichlet problem where δp_u = div(∣∇u∣^p−2∇u) is the p-Laplacian operator, Ω ⊂ R^N(N ≥ 1) is non-empty bounded open set with smooth boundary ∂Ω, p > N, λ ≥ 0, f: R → R is a continuous function and positive weight function is emphasized.