“…Moreover, the solution of (IBCP ) is explicitly given by a variation of constants formula similar to the one given in [3] in the autonomous case. We note that the operator matrices method was also used in [4,8,9] for the investigation of inhomogeneous Cauchy problems without boundary conditions.…”
In this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation.
“…Moreover, the solution of (IBCP ) is explicitly given by a variation of constants formula similar to the one given in [3] in the autonomous case. We note that the operator matrices method was also used in [4,8,9] for the investigation of inhomogeneous Cauchy problems without boundary conditions.…”
In this paper we prove the existence and the uniqueness of the classical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation.
Abstract. We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation:on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.
We find the criteria for the solvability of the operator equation AX − XB = C, where A, B, and C are unbounded operators, and use the result to show existence and regularity of solutions of nonhomogeneous Cauchy problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.