JournalszaaVol. 28 , No. 3DOI 10.4171/zaa/1385

On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts

  • Vy Khoi Le

    Missouri University of Science and Technology, Rolla, United States
  • Dumitru Motreanu

    Université de Perpignan, France
On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts cover

Abstract

This paper is concerned with the inclusion

−div(a(|∇_u_|)∇_u_) + ∂_u_ G(x, u) ∋ 0 in Ω,

with Dirichlet boundary condition u = 0 on ∂Ω, in the case where the higher order part has slow growth and the lower order part is locally Lipschitz. By using a Mountain Pass theorem for variational-hemivariational inequalities without the Palais–Smale condition in Orlicz–Sobolev spaces, we show the existence of nontrivial solutions of the above inclusion.