A Pulse Time. Banach Space The State Dependent Differential System

In many areas, such as Physics, Chemistry, Finance and so on, instantaneous sudden change phenomenon is very universal. This century, people has conducted the research about impulsive differential systems with unbounded operators on infinitude dimension spaces. While, they are systems with impulses at fixed times, for impulsive differential systems with impulses at variable times, especially, the research about the impulsive differential systems on infinitude dimension spaces with impulses depend on states have not been seen.In this thesis, we consider a class of impulsive systems with impulses depend on states and unbounded operators on infinite dimensional Banach spaces, mainly about the two typesimpulsive differential systems following:(i) Warning line model:(ii) Impulsive autonomous system:where A is the infinitesimal generator of a C₀-semigroup {T(t),t≥0} ,y₁,y₂∈X andy₁≠y₂,M,N(?)X are closed sets, and M∩N = (?),J :Mâ†'N is a mapping.To the warning line model (â… ), we introduce appropriate work space and mild solution, educe the condition of local existence property of mild solution and the condition of global existenceproperty. Especially, when f is not depends on time t, we educe the condition of pulses, namely, ifthere are two pulses on the mild solution, then the mild solution is a periodic function. To the differential system (â…¡), we introduce appropriate work space and mild solution, educe the condition of local existence property of mild solution, and the condition of global existence property, too.