Abstract

This paper is concerned with the inclusion −\mathrm{div}(a(|∇u|)∇u) + ∂_u G(x,u) \ni 0 \quad \text{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.

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