Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

Abstract

We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)

u

p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(

Δu

p−2Δu), the function φ(x, v) is of type

v

p − 2v, φ(x,v)=ddvΦ0(x,v), the potential function V: RN→ (0 , ∞ ) is continuous, and f: RN× R→ R satisfies the Carathéodory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems. © 2019, The Author(s).