Abstract
A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained. They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.
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Chiu, KS. On generalized impulsive piecewise constant delay differential equations. Sci. China Math. 58, 1981–2002 (2015). https://doi.org/10.1007/s11425-015-5010-8
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DOI: https://doi.org/10.1007/s11425-015-5010-8
Keywords
- impulsive differential equation
- piecewise constant delay of generalized type
- variation of parameters formula
- Gronwall integral inequality
- Green function
- oscillation
- nonoscillation
- stability of solutions