We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Quasilinear partial functional differential equations of the first order with nonlocal boundary condi-tions are considered. A theorem on the local existence and uniqueness of classical solutions is given. The method of bicharacteristics is used to transform the nonlocal boundary value problem into a functional integral equation and the Banach fixed-point principle to find its solution.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.