关键词: boundary value problem, delay, positive solution, p-Laplacian, schauder fixedpoint theorem

Abstract: In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φ_p（u））（t） + a（t）f（t, u（t- τ）, u（t）） = 0, 0 < t < 1;u（0） = u（0） = 0, u（1） = αu（η）;u（t） = 0,- τ≤ t ≤ 0.By using Schauder fixed-point theorem, some sufficient conditions are obtained which guarantee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.

Key words: boundary value problem, delay, positive solution, p-Laplacian, schauder fixedpoint theorem