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

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Chung N.

Annales Polonici Mathematici

2015

tom 113

nr 3

283-294

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.

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1 Annales Polonici Mathematici

1 Chung N.

1 2015

Wyniki wyszukiwania

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