[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()

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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

Author(s):

Zhang Lina¹;  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

Keywords:

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

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.

References:

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[2] Chen Y Q, Wang X D, Xu H X. Anti-periodic solutions for semilinear evolution equations [J]. Journal of Mathematical Analysis and Applications, 2002, 273(1):627-636.
[3] Aizicovici S, Mckibben M, Reich S. Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities [J]. Nonlinear Analysis, Theory, Methods and Applications, 2001, 43(1):233-251.
[4] Aftabizadeh A R, Aizicovici S, Pavel N H. Anti-periodic boundary value problems for higher order differential equations in Hilbert spaces [J]. Nonlinear Analysis, Theory, Methods and Applications, 1992, 18(3):253-267.
[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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