Existence of positive solutions for an (n+2)(n+2)-order nonlinear BVP

Under some suitable assumptions, we shall show that the (n+2)(n+2)-order nonlinear boundary value problem: (BVP){(E)[ϕp(u(n)(t))]″=f(t,u(t),u(1)(t),…,u(n+1)(t))(BC){u(i)(0)=0,i=0,1,2,…,n−3,u(n−2)(0)=ξu(n−2)(1),u(n−1)(1)=ηu(n−1)(0),u(n)(0)=μu(n)(δ),u(n)(1)=νu(n)(δ), has at least three solutions in Cn[0,1]Cn[0,1], n≥2n≥2.