Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations
By introducing subdifferentiability of lower semicontinuous convex function φ(x(t),x(t−τ)) and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomo...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/404928 |
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| _version_ | 1850174127257681920 |
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| author | Xiao-Bao Shu Yongzeng Lai Fei Xu |
| author_facet | Xiao-Bao Shu Yongzeng Lai Fei Xu |
| author_sort | Xiao-Bao Shu |
| collection | DOAJ |
| description | By introducing subdifferentiability of lower semicontinuous
convex function φ(x(t),x(t−τ)) and its conjugate function, as well
as critical point theory and operator equation theory, we obtain the existence of
multiple subharmonic periodic solutions to the following second-order nonlinear
nonautonomous neutral nonlinear functional differential equation x″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0, x(0)=0. |
| format | Article |
| id | doaj-art-d24cb3f3712847b38b6871b13dd2160c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d24cb3f3712847b38b6871b13dd2160c2025-08-20T02:19:43ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/404928404928Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential EquationsXiao-Bao Shu0Yongzeng Lai1Fei Xu2Department of Mathematics, Hunan University, Changsha 410082, ChinaDepartment of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, CanadaDepartment of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, CanadaBy introducing subdifferentiability of lower semicontinuous convex function φ(x(t),x(t−τ)) and its conjugate function, as well as critical point theory and operator equation theory, we obtain the existence of multiple subharmonic periodic solutions to the following second-order nonlinear nonautonomous neutral nonlinear functional differential equation x″(t)+x″(t−2τ)+f(t,x(t),x(t−τ),x(t−2τ))=0, x(0)=0.http://dx.doi.org/10.1155/2012/404928 |
| spellingShingle | Xiao-Bao Shu Yongzeng Lai Fei Xu Existence of Subharmonic Periodic Solutions to a Class of Second-Order Non-Autonomous Neutral Functional Differential Equations Abstract and Applied Analysis |
| title | Existence of Subharmonic Periodic Solutions to a Class of
Second-Order Non-Autonomous Neutral Functional Differential Equations |
| title_full | Existence of Subharmonic Periodic Solutions to a Class of
Second-Order Non-Autonomous Neutral Functional Differential Equations |
| title_fullStr | Existence of Subharmonic Periodic Solutions to a Class of
Second-Order Non-Autonomous Neutral Functional Differential Equations |
| title_full_unstemmed | Existence of Subharmonic Periodic Solutions to a Class of
Second-Order Non-Autonomous Neutral Functional Differential Equations |
| title_short | Existence of Subharmonic Periodic Solutions to a Class of
Second-Order Non-Autonomous Neutral Functional Differential Equations |
| title_sort | existence of subharmonic periodic solutions to a class of second order non autonomous neutral functional differential equations |
| url | http://dx.doi.org/10.1155/2012/404928 |
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