JournalszaaVol. 28, No. 3pp. 277–293

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
Download PDF

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.

Cite this article

Vy Khoi Le, Dumitru Motreanu, On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts. Z. Anal. Anwend. 28 (2009), no. 3, pp. 277–293

DOI 10.4171/ZAA/1385