Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian

In this paper, we study the existence of positive solutions of the following nth-order four-point boundary value problem with one dimensional p-Laplacian {(@f"p(u^(^n^-^1^)))^'+h(t)f(t,u(t),u^'(t),...,u^(^n^-^2^)(t))=0,0=3,u^(^i^)(0)=0,0@?i@?n-3,u^(^n^-^1^)(0)-@au^(^n^-^2^)(@x)=0,n>=3,u^(^n^-^1^)(1)+@bu^(^n^-^2^)(@h)=0,n>=3, where @f"p(s)=|s|^p^-^2s,p>1,0<@a@?1@x,0<@b@?11-@h,0<@x<@h<1. By using a fixed point theorem in cones, the existence of a positive solution and multiple positive solutions is obtained. Also, at the end of this paper, we present a generalization of this problem.

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