Uniqueness of solutions of state dependent delay differential equations
نویسندگان
چکیده
منابع مشابه
Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay
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K e y w o r d s D e l a y , Differential equation, Impulses, Fixed point. 1. I N T R O D U C T I O N The object of this paper is to present existence and uniqueness results about the solution of a system of delay-differential equations with infinitely many state-dependent impulses. This type of problem is characterized by jumps in the solution of the system. The system is (s) = / ( t , x , ) + ...
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It follows from a theorem of Veretennikov [4] that (1) has a unique strong solution, i.e. there is a unique process x(t), adapted to the filtration of the Brownian motion, satisfying (1). Veretennikov in fact proved this for a more general equation. Here we consider a different question, posed by N. V. Krylov [2]: we choose a Brownian path W and ask whether (1) has a unique solution for that pa...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1974
ISSN: 0022-247X
DOI: 10.1016/0022-247x(74)90013-4