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

Nguyen 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 -