Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay
We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form x″(z)=x(p(z)+bx′(z)). Considering a convergent power series g(z) of an auxiliary equation γ2g″(γz)g′(z)=[g(γ2z)-p(g(γz))]γg′(γz)(g′(z))2+p′′(g(z))(g′(z))3+γg′(γz)g″(z) wi...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/904679 |
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| author | Jiraphorn Somsuwan Keaitsuda Maneeruk Nakprasit |
| author_facet | Jiraphorn Somsuwan Keaitsuda Maneeruk Nakprasit |
| author_sort | Jiraphorn Somsuwan |
| collection | DOAJ |
| description | We investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form x″(z)=x(p(z)+bx′(z)). Considering a convergent power series g(z) of an auxiliary equation γ2g″(γz)g′(z)=[g(γ2z)-p(g(γz))]γg′(γz)(g′(z))2+p′′(g(z))(g′(z))3+γg′(γz)g″(z) with the relation p(z)+bx′(z)=g(γg-1(z)), we obtain an analytic solution x(z). Furthermore, we characterize a polynomial solution when p(z) is a polynomial. |
| format | Article |
| id | doaj-art-663ecda238e74874adb6eb8d9be95de8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-663ecda238e74874adb6eb8d9be95de82025-02-03T06:07:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/904679904679Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent DelayJiraphorn Somsuwan0Keaitsuda Maneeruk Nakprasit1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandWe investigate an analytic solution of the second-order differential equation with a state derivative dependent delay of the form x″(z)=x(p(z)+bx′(z)). Considering a convergent power series g(z) of an auxiliary equation γ2g″(γz)g′(z)=[g(γ2z)-p(g(γz))]γg′(γz)(g′(z))2+p′′(g(z))(g′(z))3+γg′(γz)g″(z) with the relation p(z)+bx′(z)=g(γg-1(z)), we obtain an analytic solution x(z). Furthermore, we characterize a polynomial solution when p(z) is a polynomial.http://dx.doi.org/10.1155/2015/904679 |
| spellingShingle | Jiraphorn Somsuwan Keaitsuda Maneeruk Nakprasit Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay International Journal of Mathematics and Mathematical Sciences |
| title | Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay |
| title_full | Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay |
| title_fullStr | Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay |
| title_full_unstemmed | Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay |
| title_short | Analytic Solutions of a Second-Order Functional Differential Equation with a State Derivative Dependent Delay |
| title_sort | analytic solutions of a second order functional differential equation with a state derivative dependent delay |
| url | http://dx.doi.org/10.1155/2015/904679 |
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