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∗ ...

Ω |∇u| )]p−1 ∆pu = f (u, v)+ ρ1(x) in Ω, − [ M2 (∫ Ω |∇v| )]p−1 ∆pv = g(u, v)+ ρ2(x) in Ω, ∂u ∂η = ∂v ∂η = 0 on ∂Ω, (1.1) where Ω ⊂ R,N ≥ 1, is a bounded smooth domain, 1 < p < N, η is the unit exterior vector on ∂Ω , ∆p is the p-Laplacian operator ∆pu = div(|∇u|p−2∇u) ∗ Corresponding author. E-mail addresses: [email protected], [email protected] (F.J.S.A. Corrêa), [email protected] (R.G. Na...

In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.

We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for $(\text{PS})$ condition to hold. Then prove some existence and multiplicity results using tools from Morse theory, in particular, notion cohomological local splitting eigenvalues based on Fadell-Rabinowitz index.

In the paper, we study existence of weak solutions for a class new nonlocal problems involving p x -Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, prove that id="M3"> -Kirchhoff problem has at least two nontrivial sol...