On point-dissipative systems of differential equations with quadratic nonlinearity
The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if uTAu<0 for all nontrivial zeros u of f(x).
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000108 |
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| _version_ | 1832559856875208704 |
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| author | Anile K. Bose Alan S. Cover James A. Reneke |
| author_facet | Anile K. Bose Alan S. Cover James A. Reneke |
| author_sort | Anile K. Bose |
| collection | DOAJ |
| description | The system x′=Ax+f(x) of nonlinear vector differential equations, where
the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is
point-dissipative if uTAu<0 for all nontrivial zeros u of f(x). |
| format | Article |
| id | doaj-art-bd01b8069a30498fbf720f834a7594ee |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd01b8069a30498fbf720f834a7594ee2025-02-03T01:29:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-011419911010.1155/S0161171291000108On point-dissipative systems of differential equations with quadratic nonlinearityAnile K. Bose0Alan S. Cover1James A. Reneke2Department of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USADepartment of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USADepartment of Mathematical Sciences, Clemson University, Clemson 29634-1907, SC, USAThe system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if uTAu<0 for all nontrivial zeros u of f(x).http://dx.doi.org/10.1155/S0161171291000108point-dissipativequadratic nonlinearitysymmetric matricescommutative but generally non-associative algebra. |
| spellingShingle | Anile K. Bose Alan S. Cover James A. Reneke On point-dissipative systems of differential equations with quadratic nonlinearity International Journal of Mathematics and Mathematical Sciences point-dissipative quadratic nonlinearity symmetric matrices commutative but generally non-associative algebra. |
| title | On point-dissipative systems of differential equations with quadratic nonlinearity |
| title_full | On point-dissipative systems of differential equations with quadratic nonlinearity |
| title_fullStr | On point-dissipative systems of differential equations with quadratic nonlinearity |
| title_full_unstemmed | On point-dissipative systems of differential equations with quadratic nonlinearity |
| title_short | On point-dissipative systems of differential equations with quadratic nonlinearity |
| title_sort | on point dissipative systems of differential equations with quadratic nonlinearity |
| topic | point-dissipative quadratic nonlinearity symmetric matrices commutative but generally non-associative algebra. |
| url | http://dx.doi.org/10.1155/S0161171291000108 |
| work_keys_str_mv | AT anilekbose onpointdissipativesystemsofdifferentialequationswithquadraticnonlinearity AT alanscover onpointdissipativesystemsofdifferentialequationswithquadraticnonlinearity AT jamesareneke onpointdissipativesystemsofdifferentialequationswithquadraticnonlinearity |