一类多时滞三阶p-Laplacian方程周期解的存在性问题

数学季刊 ›› 2013, Vol. 28 ›› Issue (4): 492-502.

一类多时滞三阶p-Laplacian方程周期解的存在性问题

School of Mathematical Sciences, Anhui University

收稿日期:2011-11-15 出版日期:2013-12-30 发布日期:2023-02-16
作者简介:ZHOU Ling(1988-),female,native of Funan,Anhui,a postgraduate of Anhui University, engages in functional diﬀerential equation; ZHOU Zong-fu(1964-), male, native of Hefei, Anhui, a professor of Anhui University, engages in functional diﬀerential equation(corresponding author).
基金资助:
Supported by the National Natural Science Foundation of China(11071001)； Supported by the 211 Project of Anhui University(KJTD002B)； Supported by the Natural Science Foundation of Anhui Province(1208085MAB)

Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

School of Mathematical Sciences, Anhui University

Received:2011-11-15 Online:2013-12-30 Published:2023-02-16
About author:ZHOU Ling(1988-),female,native of Funan,Anhui,a postgraduate of Anhui University, engages in functional diﬀerential equation; ZHOU Zong-fu(1964-), male, native of Hefei, Anhui, a professor of Anhui University, engages in functional diﬀerential equation(corresponding author).
Supported by:
Supported by the National Natural Science Foundation of China(11071001)； Supported by the 211 Project of Anhui University(KJTD002B)； Supported by the Natural Science Foundation of Anhui Province(1208085MAB)

摘要/Abstract

摘要： By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows (φp((x(t).. cx(t.. σ)) ′′)) ′ +f₁(x(t))x ′(t) + f₂(x ′(t))x ′′(t) +g(t, x(t), x(t.. τ(t)), ∫ ⁰_-rx(t + s) dm(s))=e(t). Some new results for existence of T-periodic solutions to such equations are obtained.

关键词: periodic solutions, deviating argument, coincidence degree, p-Laplacian equations

Abstract: By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows (φp((x(t).. cx(t.. σ)) ′′)) ′ +f1(x(t))x ′(t) + f2(x ′(t))x ′′(t) +g(t, x(t), x(t.. τ(t)), ∫ 0-rx(t + s) dm(s))=e(t). Some new results for existence of T-periodic solutions to such equations are obtained.

Key words: periodic solutions, deviating argument, coincidence degree, p-Laplacian equations

中图分类号:

O178.1

周玲, 周宗福, 沈钦锐. 一类多时滞三阶p-Laplacian方程周期解的存在性问题[J]. 数学季刊, 2013, 28(4): 492-502.

ZHOU Ling, ZHOU Zong-fu, SHEN Qin-rui. Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(4): 492-502.

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