On a Class of PDE Involving p-Biharmonic Operator

The existence of solution for a fourth-order nonlinear partial differential equation (PDE) class involving p-biharmonic operator Δ(|Δu|p−2Δu)=λρ(x)|u|q−2u in Ω, u=Δu=0, on⁡ ∂Ω, is proved by applying mountain pass theorem and a local minimization.