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

Annales Polonici Mathematici (2015)

- Volume: 113, Issue: 3, page 283-294
- ISSN: 0066-2216

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topNguyen Thanh Chung. "Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces." Annales Polonici Mathematici 113.3 (2015): 283-294. <http://eudml.org/doc/286230>.

@article{NguyenThanhChung2015,

abstract = {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.},

author = {Nguyen Thanh Chung},

journal = {Annales Polonici Mathematici},

keywords = {Kirchhoff type problems; Neumann boundary condition; Orlicz-Sobolev spaces; mountain pass theorem},

language = {eng},

number = {3},

pages = {283-294},

title = {Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces},

url = {http://eudml.org/doc/286230},

volume = {113},

year = {2015},

}

TY - JOUR

AU - Nguyen Thanh Chung

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

JO - Annales Polonici Mathematici

PY - 2015

VL - 113

IS - 3

SP - 283

EP - 294

AB - 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.

LA - eng

KW - Kirchhoff type problems; Neumann boundary condition; Orlicz-Sobolev spaces; mountain pass theorem

UR - http://eudml.org/doc/286230

ER -

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