Approximation of solutions to a delay equation with a random forcing term and non local conditions. (English) Zbl 1355.34100

Chaudhary, Renu; Pandey, Dwijendra N.

J. Integral Equations Appl. 28, No. 4, 481-507 (2016).

Summary: The existence and approximation of a solution to a delay equation with a random forcing term and non local conditions is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. Moreover, the convergence of Faedo-Galerkin approximations of the solution is shown. An example is given which illustrates the results.

MSC:

34K07	Theoretical approximation of solutions to functional-differential equations
34K30	Functional-differential equations in abstract spaces
34K50	Stochastic functional-differential equations
34K10	Boundary value problems for functional-differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

analytic semigroup; Faedo-Galerkin approximations; Hilbert space; mild solution; delay equation with a random forcing term