Generalized ODE approach to impulsive retarded functional differential equations
By Márcia Federson, Š. Schwabik. Differential and Integral Equations, 2006
58 citations recorded by the source corpus.
It is known that retarded functional differential equations (RFDEs) can be regarded as generalized ordinary differential equations (we write GODEs). See [2, 6, 7]. In this paper, we prove the equivalence between RFDEs with pre-assigned moments of impulse effects and a certain class of GODEs introduced in [8] using some ideas of [2, 6, 7]. We state results on the existence, uniqueness and continuous dependence of solutions for this class of GODEs and we use them to obtain fine results concerning the corresponding impulsive RFDEs.
Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/def1ab2aa80e3929c2f8b7d6c6e24db47f2cf28d
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In Applied Mathematics
In Control and Systems Engineering
In Numerical Analysis
Citations in the corpus
- Basic results for functional differential and dynamic equations involving impulses (2013, methodology): “[7,8]) that it is sufficient to impose certain conditions on the indefinite integral of the function on the right-hand side of (1.”
- Dynamic equations on time scales and generalized ordinary differential equations (2012, background): “For example, the recent papers [3] and [4] demonstrate the possibility of converting retarded functional differential equations to generalized ordinary differential equations for functions with values in a Banach space.”
- Measure functional differential equations and functional dynamic equations on time scales (2012, methodology): “Schwabik in the paper [6], which is devoted to impulsive retarded functional differential equations.”