التفاصيل البيبلوغرافية
| العنوان: |
A characterization of solutions in linear differential equations with periodic forcing functions. |
| المؤلفون: |
Kato, J., Naito, T., Shin, J. S. |
| المصدر: |
Journal of Difference Equations & Applications; Jan2005, Vol. 11 Issue 1, p1-19, 19p |
| مصطلحات موضوعية: |
DIFFERENTIAL equations, LINEAR systems, MATRICES (Mathematics), EXPONENTIAL functions, DIFFERENCE equations, BEHAVIOR |
| مستخلص: |
We deal with periodic linear inhomogeneous differential equations of the form d x /d t = Ax ( t )+ f ( t ), where A is an m × m matrix and f a τ-periodic continuous function. The solutions of this equation will be characterized as a sum of τ-periodic functions and exponential-like functions in an explicit form. As applications of this result, we can obtain the complete classification of the set of initial values according to the behavior of solutions: bounded solutions on [0, ∞], τ-periodic solutions, quasi-periodic solutions, asymptotically periodic solutions and solutions with the growth order as t →∞ , etc. The essential part of our method is to give a specific representation of the solutions of difference equations corresponding to the above equations. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
Complementary Index |
