Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces

Nguyen Thanh Chung

Annales Polonici Mathematici, Tome 113 (2015), p. 283-294 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider Kirchhoff type problems of the form ⎧ -M(ρ(u))(div(a(|∇u|)∇u) - a(|u|)u) = K(x)f(u) in Ω ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω where $Ω ⊂ ℝ^{N}$, N ≥ 3, is a smooth bounded domain, ν is the outward unit normal to ∂Ω, $ρ(u)= ∫_{Ω} (Φ(|∇u|) + Φ(|u|))dx$, M: [0,∞) → ℝ is a continuous function, $K ∈ L^{∞}(Ω)$, and f: ℝ → ℝ is a continuous function not satisfying the Ambrosetti-Rabinowitz type condition. Using variational methods, we obtain some existence and multiplicity results.

Détail

Publié le : 2015-01-01

Zbl 1326.35105

EUDML-ID : urn:eudml:doc:286230