The iterative solutions for some fourth-order pp-Laplace equation boundary value problems

In this paper, the fourth-order four-point pp-Laplace equation boundary value problem [φp(u″(x))]″=f(x,u(x),u″(x)),0≤x≤1,u(0)=0,u(1)=au(ξ),u″(0)=0,u″(1)=bu″(ζ), is studied, where φp(t)=|t|p−2⋅t,p>1;0<ξ,ζ<1φp(t)=|t|p−2⋅t,p>1;0<ξ,ζ<1; f∈C([0,1]×R2,R)f∈C([0,1]×R2,R). The existence of iterative solutions is obtained via the lower and upper solution method.