Existence of positive solutions for n+2n+2 order pp-Laplacian BVP

Under some suitable assumptions, we show that the n+2n+2 order non-linear boundary value problems (BVP1){(E1)[ϕp(u(n)(t))]″=f(t,u(t),u(1)(t),…,u(n+1)(t))(BC1){u(i)(0)=0,i=0,1,2,…,n−3,u(n−1)(1)=0u(n−2)(0)=λu(n−1)(η)u(n+1)(0)=α1u(n+1)(ξ)u(n)(1)=β1u(n)(ξ) and (BVP2){(E2)[ϕp(u(n)(t))]″=f(t,u(t),u(1)(t),…,u(n+1)(t))(BC2){u(i)(0)=0,i=0,1,2,…,n−3,u(n−1)(0)=0u(n−2)(1)=−λu(n−1)(η)u(n+1)(0)=α1u(n+1)(ξ)u(n)(1)=β1u(n)(ξ) have at least two positive solutions in Cn[0,1]Cn[0,1].