Geodesic
On a Class of Impulsive Functional-Differential Equations with Nonatomic Difference Operator
Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 37-49

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We establish conditions for the existence and uniqueness of the solutions of nonlinear functional-differential equations with impulsive action in a Banach space. The equation under consideration is not solved for the derivative. It is assumed that the characteristic operator pencil corresponding to the linear part of the equation satisfies a constraint of parabolic type in the right half-plane. Applications to partial functional-differential equations not of Kovalevskaya type are considered.
Keywords: impulsive functional-differential equation, nonatomic difference operator, equation of Sobolev type, equation not of Kovalevskaya type, Sobolev space, operator pencil, Banach space. 
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     author = {L. A. Vlasenko and A. G. Rutkas},
     title = {On a {Class} of {Impulsive} {Functional-Differential} {Equations} with {Nonatomic} {Difference} {Operator}},
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L. A. Vlasenko; A. G. Rutkas. On a Class of Impulsive Functional-Differential Equations with Nonatomic Difference Operator. Matematičeskie zametki, Tome 95 (2014) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/MZM_2014_95_1_a3/