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We investigate a class of abstract functional integro-differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions. Also, related convergence results are established and an example arising in the mathematical… (More)

- Eduardo Hernández Morales, Mark A. McKibben, Hernán R. Henríquez
- Mathematical and Computer Modelling
- 2009

We investigate a class of abstract stochastic evolution equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space. We establish the existence and uniqueness of a mild solution, a continuous dependence estimate, and various convergence and approximation results. Finally, the… (More)

- Eduardo Hernández Morales, Mark A. McKibben
- Applied Mathematics and Computation
- 2007

In this paper, we study the existence of mild solutions for a class of abstract partial neutral functional–differential equations with state-dependent delay. 2006 Elsevier Inc. All rights reserved.

second-order damped McKean-Vlasov stochastic evolution equations N.I. Mahmudov aand M.A. McKibben b,∗ aDepartment of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TURKEY bGoucher College, Mathematics and Computer Science Department, Baltimore, MD 21204, U S A Abstract We establish results concerning the global existence,… (More)

- MARK A. McKIBBEN
- 2004

in a real separable Hilbert space H , where the linear (possibly multivalued) operator A : D(A) ⊂H →H is the infinitesimal generator of a strongly continuous cosine family on H , W is a K-valued Wiener process with incremental covariance given by the nuclear operator Q defined on a complete probability space (Ω, ,P) equipped with a normal filtration (… (More)

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7]… (More)

We study a class of nonlinear stochastic partial differential equations arising in themathematical modeling of the transversemotion of an extensible beam in the plane. Nonlinear forcing terms of functional-type and those dependent upon a family of probability measures are incorporated into the initial-boundary value problem (IBVP), and noise is incorporated… (More)

Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding… (More)

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