Positive Solutions for Fourth-order Delay Differential Equation of Boundary Value Problem with p-Laplacian

ZHANG Yu-chuan, ZHOU Zong-fu

doi:10.13371/j.cnki.chin.q.j.m.2014.02.003

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 2: 171 - 179

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.003

Positive Solutions for Fourth-order Delay Differential Equation of Boundary Value Problem with p-Laplacian

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School of Mathematical Sciences, Anhui University

ZHANG Yu-chuan(1985-), male, native of Nanyang, Henan, M.S.D., engages in boundary value problem.

Received date: 2012-03-06

Online published: 2020-12-01

Supported by

Supported by the National Natural Science Foundation of China(10801001)； Supported by the Natural Science Foundation of Anhui Province(1208085MA13,KJ2009A005Z)；

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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

Cite this article

ZHANG Yu-chuan, ZHOU Zong-fu . Positive Solutions for Fourth-order Delay Differential Equation of Boundary Value Problem with p-Laplacian[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(2) : 171 -179 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.003

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