Existence of positive solutions top-Kirchhoff-type problem without compactness conditions

Existence of a positive solution to Kirchhoff type problems without compactness conditions

Article history: Received 20 February 2012 Revised 18 May 2012 Available online 30 May 2012

EXISTENCE OF POSITIVE SOLUTIONS FOR A QUASILINEAR ELLIPTIC SYSTEM OF p–KIRCHHOFF TYPE

In this paper, we consider the existence of positive solutions to the following p Kirchhoff-type system ⎧⎪⎨⎪⎪⎩ −M (∫ Ω |∇u|pdx ) Δpu = g(x)|u|q−2u+ α α+β |u|α−2u|v|β , x ∈Ω, −M (∫ Ω |∇u|pdx ) Δpv = h(x)|v|q−2v+ β α+β |u|α |v|β−2v, x ∈Ω, u = v = 0, x ∈ ∂Ω, where Ω is a bounded domain in RN , M(s) = a + bsk , Δpu = div(|∇u|p−2∇u) is the p Laplacian operator, α > 1 , β > 1 , 1 < p < q < α +β < p∗ ...

Positive solutions of Schrödinger-Kirchhoff-Poisson system without compact condition

Existence and multiplicity of positive solutions for a class of p(x)-Kirchhoff type equations

* Correspondence: [email protected] Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China Abstract In this article, we study the existence and multiplicity of positive solutions for the Neumann boundary value problems involving the p(x)-Kirchhoff of the form ⎪⎨⎪⎩ −M (∫ 1 p(x) (|∇u|p(x) + λ|u|p(x))dx ) (div (|∇u|p(x)−2∇u) − λ|u|p(x)−2u) = f (x, u) in , ∂u ∂v = 0...

Existence of positive solutions to Kirchhoff type problems with zero mass

Article history: Received 16 May 2013 Available online 26 August 2013 Submitted by V. Radulescu