The Disturbance Of Elliptic Equations Existence And Multiplicity

The aim of this article is to study a perturbed p-biharmonic equation depending of two real parameters, where λ,μ∈[0,+∞[,Ω,(?)RN(N≥1) is a non-empty bounded open set with a sufficient smooth boundary (?)Ω,, p>1.f,g:Ω×Râ†'R are Caratheodory functions. We establish the existence of at least three solutions for this problem based on variational methods.Moreover, the existence of at least one non-trivial solution to a boundary value problem for p-Laplacian equations, where λ∈[0,+∞[,Ω(?)RN(N≥1) is a open set with sufficient smooth boundary (?)Ω, p>N. f:Ω×Râ†'R is a L1-Caratheodory function, under a non-standard growth condition of the nonlinear term, is established. No asymptotic condition on the nonlinear term either at zero or at infinity is requested. Our approach is based on a local minimum theorem for differentiable functionals.