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 author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the...The author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the systems. Compared with the previous works finished by Lakshmikantham and Erbe, the author's results do not require the right handed function and impulsive functions with special structures such as monotonicity, etc. When the impulsive effects are absent, these results could be viewed as new generalized forms of the two so called optimal results about second order scalar differential equations derived by Lees and Mawhin respectively.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.
文摘The author introduces a concept of curvature bound set relative to second order impulsive differential systems and based on this concept discusses the existence of solutions to the Picard boundary value problem of the systems. Compared with the previous works finished by Lakshmikantham and Erbe, the author's results do not require the right handed function and impulsive functions with special structures such as monotonicity, etc. When the impulsive effects are absent, these results could be viewed as new generalized forms of the two so called optimal results about second order scalar differential equations derived by Lees and Mawhin respectively.
