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. 277–293DOI 10.4171/ZAA/1385