\(L_ p\)-equivalence of impulsive equations
In a Banach space X, consider the differential equation with impulses \(dx/dt=F(t,x)\), \(x(t_ n+0)=Q_ nx(t_ n)\), with the given infinite sequence \(t_ n\to \infty\). The function F is assumed continuous and the operators \(Q_ n\) are bounded linear. Consider also another similar system, as ``perturbed system''; these two systems are called \(L_ p\)- equivalent if, within some specified neighborhoods, for each solution of the first system there is a solution of the second system such that the difference is \(L_ p\)-integrable. The two systems are called asymptotically \(L_ p\)-equivalent if this happens in some interval \((t_ 0,\infty)\). This paper gives a set of sufficient conditions for two such systems to be \(L_ p\)-equivalent and to be asymptotically \(L_ p\)-equivalent. It discusses these conditions and hints at possible extensions.
scientific article; zbMATH DE number 4097868