Abstract
Leta,bbe two integers withb-a≥5and let𝕋2={a+2,a+3,…,b-2}. We show the existence of solutions for nonlinear fourth-order discrete boundary value problemΔ4u(t-2)=f(t,u(t),Δ2u(t-1)),t∈𝕋2,u(a+1)=u(b-1)=Δ2u(a)=Δ2u(b-2)=0under a nonresonance condition involving two-parameter linear eigenvalue problem. We also study the existence and multiplicity of solutions of nonlinear perturbation of a resonant linear problem.
Highlights
The deformations of an elastic beam whose both ends are supported are described by a fourth-order two-point boundary value problem ygxyex, 0 < x < 1, 1.1 y0 y1 y 0 y 1 0See studies by Aftabizadeh 1 and Gupta in 2
The purpose of this paper is to show that the answer is yes
Relatively little is known about the existence of solutions of fourth-order discrete boundary value problems
Summary
The deformations of an elastic beam whose both ends are supported are described by a fourth-order two-point boundary value problem ygxyex , 0 < x < 1, 1.1 y0 y1 y 0 y 1 0See studies by Aftabizadeh 1 and Gupta in 2. Relatively little is known about the existence of solutions of fourth-order discrete boundary value problems.
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