Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument
We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/507854 |
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| author | Zaihong Wang Jin Li Tiantian Ma |
| author_facet | Zaihong Wang Jin Li Tiantian Ma |
| author_sort | Zaihong Wang |
| collection | DOAJ |
| description | We study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation. |
| format | Article |
| id | doaj-art-313ed797241648a7b785be757f8bf69c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-313ed797241648a7b785be757f8bf69c2025-08-20T02:38:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/507854507854Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating ArgumentZaihong Wang0Jin Li1Tiantian Ma2School of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaWe study the existence of periodic solutions of the second-order differential equation x′′+ax+-bx-+g(x(t-τ))=p(t), where a,b are two constants satisfying 1/a+1/b=2/n, n∈N, τ is a constant satisfying 0≤τ<2π, g,p:R→R are continuous, and p is 2π-periodic. When the limits limx→±∞g(x)=g(±∞) exist and are finite, we give some sufficient conditions for the existence of 2π-periodic solutions of the given equation.http://dx.doi.org/10.1155/2013/507854 |
| spellingShingle | Zaihong Wang Jin Li Tiantian Ma Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument Abstract and Applied Analysis |
| title | Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument |
| title_full | Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument |
| title_fullStr | Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument |
| title_full_unstemmed | Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument |
| title_short | Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument |
| title_sort | periodic solutions of duffing equation with an asymmetric nonlinearity and a deviating argument |
| url | http://dx.doi.org/10.1155/2013/507854 |
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