MULTIPLE SOLUTIONS FOR THE NONHOMOGENEOUS FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Multiple solutions for a fourth-order nonlinear elliptic problem

The existence of multiple solutions for a class of fourth-order elliptic equation with respect to the generalized asymptotically linear conditions is established by using the minimax method and Morse theory.

MULTIPLE NONNEGATIVE SOLUTIONS FOR BVPs OF FOURTH-ORDER DIFFERENCE EQUATIONS

First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t− 2) = a(t) f (x(t)), t ∈ [2,T], x(0)= x(T +2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known LeggettWilliams fixed point theorem, and then, for arbitrary positive integerm, existence results for at least 2m− 1 nonnegative solutions are ...

Multiple Solutions for a Fourth Order Elliptic Equation with Hardy Type Potential

Consider the fourth order elliptic equation with Hardy type potential { ∆2u = μ |x|4a(x)u+ λb(x)f(u) in Ω, u = 0, ∂u ∂ν = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 5), is a bounded domain with smooth boundary ∂Ω, 0 ∈ Ω, ν is the outward unit normal to ∂Ω, the weighted function a : Ω → R may change sign, λ, μ are two parameters. Under suitable conditions on the nonlinearities, a multiplicity result is given us...

Positive Solutions for a Nonlocal Fourth Order Equation of Kirchhoff Type

Existence and multiplicity of positive solutions for the fourth order equation u′′′′ − M( ∫ 1 0 |u ′|2 dx)u′′ = q(x)f(x, u, u′), which models simply supported extensible beams, are considered using fixed point theorems in cones of ordered Banach spaces.