JOURNAL Series A - Pure and Applied Mathematics
JOURNAL Series A - Pure and Applied Mathematics
JOURNAL Series A - Pure and Applied Mathematics
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c○Journal of Technical University at PlovdivFundamental Sciences <strong>and</strong> Applications, Vol. 11, 2005-2006<strong>Series</strong> A-<strong>Pure</strong> <strong>and</strong> <strong>Applied</strong> <strong>Mathematics</strong>Bulgaria, ISSN 1310-8271Nonlinear Semigroup for NonlinearAbstract Impulse Differential EquationsAt. Georgieva, St. KostadinovAbstractA semigroup induced by the Poincaré map of the nonlinear abstract impulsedifferential equationdxdt = A(t)x + f(t, x), (t ≠ t n)x(t + n ) = Q n x(t n ) + h n (x(t n )), (t = t n )with possibly unbounded linear operators A(t) <strong>and</strong> Q n is considered.1 IntroductionImpulse equations are useful mathematical models of many processes in all branchesof the physics, which suddenly change their state at certain moments. In the mathematicalsimulation is often possibly the change to neglecte <strong>and</strong> assume that thechange takes place by jumps.The qualitative theory of these equations has been intensively developing in thelast 5 years (see for examples [2]-[7]). In this paper are considered nonlinear abstractimpulse differential equations <strong>and</strong> semigroups induced by the the Poincaré map.0 2000 <strong>Mathematics</strong> Subject Classification: 34A37, 34G10, 34C25 .0 Key words <strong>and</strong> phrases: Impulse differential equations, nonlinear semigroups.0 Received June 15, 200655
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