1. Measure solutions for impulsive evolution equations with measurable vector fields
- Author
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N. U. Ahmed
- Subjects
Generalization ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Banach space ,Semilinear equations ,01 natural sciences ,Measure (mathematics) ,010101 applied mathematics ,Nonlinear system ,Differential inclusion ,Cover (topology) ,Measure solutions ,Bounded function ,Finitely additive measures ,Semigroups of operators ,Vector field ,0101 mathematics ,Discontinuous vector fields ,Analysis ,Mathematics - Abstract
In this paper we present some results on the question of existence of generalized or measure valued solutions for semilinear impulsive evolution equations on Banach spaces with the nonlinear parts being merely measurable and bounded on bounded sets. This is a far reaching generalization of the previous results of the author and others. It may be interesting to consider extension of the results of this paper to cover impulsive differential inclusions and their potential applications to control theory and uncertain dynamics.
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