Properties of solutions to a second order nonlinear differential equation
In this note, we show when all solutions to the nonlinear differential equation x″+c(t)f(x)g(x′)x′+a(t,x)=0 are bounded. Furthermore, the solutions are either oscillatory or monotonic and asymptotically stable.
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171290001156 |
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| _version_ | 1832554856772009984 |
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| author | Allan J. Kroopnick |
| author_facet | Allan J. Kroopnick |
| author_sort | Allan J. Kroopnick |
| collection | DOAJ |
| description | In this note, we show when all solutions to the nonlinear differential equation x″+c(t)f(x)g(x′)x′+a(t,x)=0 are bounded. Furthermore, the solutions are either oscillatory or monotonic and asymptotically stable. |
| format | Article |
| id | doaj-art-9eb5c79b3e8f4505beabfa4ba0bc34c8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9eb5c79b3e8f4505beabfa4ba0bc34c82025-02-03T05:50:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113482182310.1155/S0161171290001156Properties of solutions to a second order nonlinear differential equationAllan J. Kroopnick0Office of Retirement and Survivors Insurance, Social Security Administration, 3-D-22 Operations Building, 6401 Security Boulevard, Baltimore, Maryland 21235, USAIn this note, we show when all solutions to the nonlinear differential equation x″+c(t)f(x)g(x′)x′+a(t,x)=0 are bounded. Furthermore, the solutions are either oscillatory or monotonic and asymptotically stable.http://dx.doi.org/10.1155/S0161171290001156 |
| spellingShingle | Allan J. Kroopnick Properties of solutions to a second order nonlinear differential equation International Journal of Mathematics and Mathematical Sciences |
| title | Properties of solutions to a second order nonlinear differential equation |
| title_full | Properties of solutions to a second order nonlinear differential equation |
| title_fullStr | Properties of solutions to a second order nonlinear differential equation |
| title_full_unstemmed | Properties of solutions to a second order nonlinear differential equation |
| title_short | Properties of solutions to a second order nonlinear differential equation |
| title_sort | properties of solutions to a second order nonlinear differential equation |
| url | http://dx.doi.org/10.1155/S0161171290001156 |
| work_keys_str_mv | AT allanjkroopnick propertiesofsolutionstoasecondordernonlineardifferentialequation |