[1] Zhang Lina, Xue Xingmei,. Anti-periodic solutions to a classof second-order evolution equations [J]. Journal of Southeast University (English Edition), 2003, 19 (4): 432-436. [doi:10.3969/j.issn.1003-7985.2003.04.027]

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Anti-periodic solutions to a classof second-order evolution equations()

关于一类二阶发展方程的反周期解

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 4

Page:

432-436

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-12-30

Info

Title:

Anti-periodic solutions to a classof second-order evolution equations

关于一类二阶发展方程的反周期解

Author(s):

Zhang Lina^{1, 2}, Xue Xingmei¹

¹Department of Mathematics, Southeast University, Nanjing 210096, China
²Department of Mathematics and Physics, Anhui University of Science and Technology, Huainan 232001, China

张莉娜^{1, 2}, 薛星美¹

¹东南大学数学系, 南京 210096; ²安徽理工大学数理系, 淮南 232001

Keywords:

maximal monotone operator;  anti-periodic solution;  Poincaré inequality;  second-order evolution equations

极大单调算子;  反周期解;  Poincaré不等式;  二阶发展方程

PACS:

O175.8

DOI:

10.3969/j.issn.1003-7985.2003.04.027

Abstract:

In this paper we discuss the anti-periodic problem for a class of abstract nonlinear second-order evolution equations associated with maximal monotone operators in Hilbert spaces and give some new assumptions on operators. We establish the existence and uniqueness of anti-periodic solutions, which improve andgeneralize the results that have been obtained.Finally we illustrate the abstract theory by discussing a simple example of an anti-periodic problem for nonlinear partial differential equations.

本文研究了在Hilbert空间中与极大单调算子族相联系的抽象的二阶发展方程的反周期问题, 给出了关于算子族{A(t):0≤t≤T}的新的假设, 并在此假设下证明了反周期解的存在性与惟一性, 推广了已有的结果.最后给出一个例子说明抽象的反周期问题在非线性偏微分方程中的简单应用.

References:

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[5] Aizicovici S, Pavel N H. Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space [J]. Journal of Functional Analysis, 1991, 99(2):387-408.
[6] Aftabizadeh A R, Aizicovici S, Pavel N H. On a class of second-order anti-periodic boundary value problems [J]. Journal of Mathematical Analysis and Applications, 1992, 171(1):301-321.
[7] Xue X M, Song G Z, Ma J P. Second order nonlinear evolution equations in Banach spaces [J]. Journal of Mathematical Analysis and Applications, 1995, 194(1):1-13.
[8] Kartsatos A G, Parrott M E. The weak solution of a functional differential equation in a general Banach spaces [J]. Journal of Differential Equations, 1988, 75(2):290-302.
[9] Kartsatos A G, Parrott M E. Convergence of the Kato approximates for evolution equations involving functional perturbations [J]. Journal of Differential Equations, 1983, 47(3):358-377.
[10] Barbu V. Nonlinear semigroups and differential equations in Banach spaces[M]. Noordhoff: Leyden, 1976.

Memo

Memo:

Biographies: Zhang Lina(1977—), female, graduate; Xue Xingmei(corresponding author), male, doctor, associate professor, xmxue@seu.edu.cn.

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