Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces

Abstract

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation −div(φ(|∇u|)∇u) = f (x, u) + h in Ω under Dirichlet boundary conditions, where Ω ⊂ R N is a bounded smooth domain, φ : (0, ∞) −→ (0, ∞) is a suitable continuous function and f : Ω × R → R satisfies the Carathéodory conditions, while h : Ω → R is a measurable function.