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...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.展开更多
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions ...The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.展开更多
By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic s...By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.展开更多
文摘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.
基金Project supported by Natural Science Foundation of Guangdong (011471)Foundation for the study of Natural Science for Universities of Guangdong (0120).
文摘The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
基金This work is partially supported by the Natural Sciences Foundation of P.R.China under Grant10061004the ABRF of Yunnan Province, P.R.China.
文摘By using the concept of almost periodic 'sequence', that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.
