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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 3, 2009, pp. 277–293
DOI: 10.4171/ZAA/1385

Published online: 2009-09-30

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

Vy Khoi Le[1] and Dumitru Motreanu[2]

(1) Missouri University of Science and Technology, Rolla, United States
(2) Université de Perpignan, France

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.

Keywords: Variational-hemivariational inequality, Orlicz–Sobolev space, Mountain Pass theorem, linking theorem

Le Vy Khoi, Motreanu Dumitru: On Nontrivial Solutions of Variational-Hemivariational Inequalities with Slowly Growing Principal Parts. Z. Anal. Anwend. 28 (2009), 277-293. doi: 10.4171/ZAA/1385