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 8>>< >>: . p.u.n􀀀1///0 C h.t/f .t; u.t/; u0.t/; : : : ; u.n􀀀2/.t// D 0; 0 < t < 1; n 3; u.i/.0/ D 0; 0 i n 􀀀 3; u.n􀀀1/.0/ 􀀀 u.n􀀀2/. / D 0; n 3; u.n􀀀1/.1/ C u.n􀀀2/. / D 0; n 3; where p.s/ D jsjp􀀀2s; p > 1; 0 < 1 ; 0 < 1 1􀀀 ; 0 < < < 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.