| Title | EVENTUAL PRACTICAL STABILITY AND CONE VALUED LYAPUNOV FUNCTIONS FOR DIFFERENTIAL EQUATIONS WITH “MAXIMA” |
| Publication Type | Journal Article |
| Year of Publication | 2010 |
| Authors | HENDERSON, JOHNNY, HRISTOVA, SNEZHANA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 14 |
| Issue | 4 |
| Start Page | 515 |
| Pagination | 524 |
| Date Published | 12/2010 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 34D20 |
| Abstract | A special type of practical stability for differential equations with “maxima” is introduced. The definitions incorporate two different measures and a scalar product on a cone. The application of a dot product allows us to use scalar comparison of ordinary differential equations for investigation of stability properties of the solutions. At the same time, the fixed vector, involved in the definition, plays a role of a weight of the components of the solution. Some sufficient conditions for eventual d-practical stability in terms of two measures of nonlinear differential equations with “maxima” are obtained. The proofs are based on the Razumikhin method and cone valued Lyapunov functions. An example illustrates the practical application of the proven results and the advantage of the introduced type of stability.
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| URL | http://www.acadsol.eu/en/articles/14/4/8.pdf |
| Short Title | DIFFERENTIAL EQUATIONS WITH “MAXIMA” |
| Refereed Designation | Refereed |
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