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Oscillatory solutions of differential equations with several discrete delays and generalized ODEs by Marielle Ap. Silva; Márcia Federson is a Mathematics article available to read on EtoBox.
What is Oscillatory solutions of differential equations with several discrete delays and generalized ODEs about?
The study of models which deal with oscillating functions is of great importance in Physics and other sciences. In this work, we are interested in investigating the oscillatory behavior of solutions of delay differential equations subject to impulsive effects and having righthand sides which admit not only many discontinuities but also oscillations. We use the framework of Kurzweil-Henstock and Kurzweil-Henstock-Stieltjes integrals to deal with the integral form of our equations. We establish conditions for all solutions of our linear delay differential equation to be oscillatory. Not only that, but we also deal with generalized ODEs as introduced by Jaroslav Kurzweil, since the latter encompass delay differential equations. We prove an important result which relates oscillatory solutions around zero of retarded Volterra-Stieltjes-type integral equations to oscillatory solutions around zero of the corresponding generalized ODEs. Moreover, an oscillatory criterion not necessarily around zero for linear homogeneous generalized ODEs is obtained. Some examples are brought about in order to illustrate the results. Keywords Delay differential equations
Who reads Oscillatory solutions of differential equations with several discrete delays and generalized ODEs?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Marielle Ap. Silva; Márcia Federson
- Publisher
- Springer Science and Business Media LLC
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)