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On a new class of abstract impulsive differential equations
Proceedings of the American Mathematical Society · 2012 · Vol. 141(5) · pp. 1641–1649
Eduardo Hernández✉(Universidade de São Paulo)Donal O’Regan(Ollscoil na Gaillimhe – University of Galway)
Abstract
In this note we introduce a new class of abstract impulsive differential equations for which the impulses are not instantaneous. We introduce the concepts of mild and classical solution and we establish some results on the existence of these types of solutions. An example involving a partial differential equation is presented.
Nonlinear Differential Equations AnalysisStability and Controllability of Differential EquationsDifferential Equations and Numerical MethodsClass (philosophy)MathematicsDifferential equationFirst-order partial differential equationMathematical analysisMethod of characteristicsPartial differential equationApplied mathematicsDifferential (mechanical device)Computer science
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