Multiple Solutions of Some Nonlinear Variational Problems

Abstract

Abstract The aim of this paper is to prove some existence and multiplicity results for functionals of type J(u) = ∫Ω­ A(x, u)|▽u|2dx - ∫Ω­ G(x, u)dx, u 2 D ∊ H0 1 (Ω), with bounded domain Ω in ℝN. Since, in general, J is not Gâteaux differentiable in D, we study its restriction on the Banach space X = H0 1 (Ω) ∩ L∞(Ω) and apply some abstract existence and multiplicity theorems involving a variant of condition (C) below.