Periodic Boundary Value Problem for First Order Differential Equations with Impulses at Variable Times
نویسندگان
چکیده
There exist several papers about boundary value problems with impulŽ sive effects at fixed points, but the different techniques employed for w x w x instance, limit arguments in 1, 3 , topological degree 10 , fixed point w x w x. theorems 9 or set-valued maps 2 do not seem applicable to problems with impulses at variable times. Ž w x. Recently, some comparison principles have appeared see 4, 8 for impulsive differential equations at variable times. Our aim consists in applying these principles and introducing some new results in this direction to develop the method of upper and lower solutions in order to find an existence result for the following periodic boundary value problem with impulses at variable times, u9 t s f t , u t , t g J , t / g u t 1.1 Ž . Ž . Ž . Ž . Ž . Ž . u tq s u t q I u t , t s g u t , 1.2 Ž . Ž . Ž . Ž . Ž . Ž . Ž . u 0 s u T , 1.3 Ž . Ž . Ž . w x Ž . 1Ž y. 1Ž . where J s 0, T , f g C J = R, R , I g C R, R , and g g C R, R .
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تاریخ انتشار 1996