Research Journal Articles
 
published OR in-press,  submitted,   in progress:

 

  1. Balasubramaniam, P, Hernandez, E., and McKibben, M., On stochastic state-dependent neutral functional evolution equations, in progress.

  2. Keck, D. and McKibben, M., Stochastic McKean-Vlasov evolution equations driven by fractional Brownian motion, in progress.

  3. Hernandez, E., Henriquez, H., and McKibben, M., Existence results for abstract impulsive second-order neutral functional differential equations, submitted.

  4. Hernandez, E., Henriquez, H., and McKibben, M., Existence of solutions of second-order partial neutral functional differential equations with unbounded delay, submitted.

  5. Hernandez, E. and McKibben, M., Existence of solutions of second-order implicit functional differential equations with unbounded delay, submitted.

  6. Mahmudov, N. I. and McKibben, M., On a class of backward McKean-Vlasov stochastic equations in Hilbert space: Existence and convergence properties, submitted.

  7. Balasubramaniam, P, McKibben, M., and V. Kumar, A general existence result for abstract neutral stochastic functional integro-differential infinite delay systems, submitted.

  8. Keck, D. and McKibben, M., Abstract stochastic Ito-Volterra evolution equations, to appear in Journal of Applied Mathematics and Stochastic Analysis.

  9. Mahmudov, N. I. and McKibben, M., On backward stochastic evolution equations in Hilbert space and optimal control, to appear in Nonlinear Analysis: Theory, Methods, and Applications.

  10. Hernandez, E. and McKibben, M., On state-dependent partial neutral functional differential equations , to appear in Applied Mathematics and Computation.

  11. Mahmudov, N. I. and McKibben, M., McKean-Vlasov stochastic differential equations in Hilbert spaces under Caratheodory conditions, to appear in Dynamic Systems and Applications.

  12. Mahmudov, N. I. and McKibben, M., Approximate controllability of second-order neutral stochastic evolution equations, to appear in Discrete, Continuous, and Impulsive Dynamic Systems and Applications.

  13. Mahmudov, N. I. and McKibben, M.,  Abstract second-order damped McKean-Vlasov stochastic evolution equations, Stochastic Analysis and Applications, vol. 24, no. 2, (2006), 303 - 328.

  14. Hernandez, E. and McKibben, M., Some comments on: Existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations, Computers and Mathematics with Applications, vol. 50, no. 8-9, (2005), 655 - 669.

  15. Keck, D. and McKibben, M., Abstract stochastic integro-differential delay equations, Journal of Applied Mathematics and Stochastic Analysis, vol. 2005 no. 3, (Dec 2005), 271 - 306.

  16. McKibben, M., Second-order neutral stochastic evolution equations with heredity,     Journal of Applied Mathematics and Stochastic Analysis, vol. 17, no. 2, (Sept. 2004), 172 - 199. 

  17. Keck, D. and McKibben, M., On a McKean-Vlasov stochastic integro-differential evolution equation of Sobolev-type,  Journal of Stochastic Analysis and Applications, vol. 2, no. 5, (Oct. 2003), 1115 - 1139.

  18. Keck, D. and McKibben, M., Functional integro-differential stochastic evolution equations in Hilbert space,  Journal of Applied Mathematics and Stochastic Analysis, vol. 16, (Nov. 2003), 1 - 21.

  19. McKibben, M., Second-order damped functional stochastic evolution equations in Hilbert space, Dynamic Systems and Applications, vol. 12, no. 3 - 4, (Dec. 2003), 467 - 488.

  20. McKibben, M., Approximate controllability results for a class of abstract second-order functional evolution equations, Journal of Optimization Theory and Applications, vol. 117, no. 2, (May 2003), 397 - 414.

  21. McKibben, M., A note on the approximate controllability of a class of abstract semi-linear evolution equations,  Far East Journal of Math. Sci., vol. 5, issue 2, May 2002, 113 - 133.

  22. Aizicovici, S., McKibben, M., and Reich, S., Anti-periodic solutions to non-monotone evolution equations with discontinuous nonlinearities, Nonlinear Analysis, vol 43, no. 2, Jan (2001), 233 - 251.

  23. McKibben, M., Controllability of abstract evolution systems with nonlocal initial data.  Far East J. of Appl. Math., vol. 4, no. 3, Nov. (2000), 317 – 343.

  24. McKibben, M., On some nonlinear nonlocal autonomous Cauchy problems in Banach spaces, Far East J. of Math. Sc., vol 2., no. 4, July (2000), 555 - 575. 

  25. Aizicovici, S., Grasselli, M., and McKibben, M., A hyperbolic integro-differential system related to phase field models, Adv. Math. Sci. Appl., vol. 10, no. 2 (2000), 601 – 625. (Also available as Technical Report #367P, Politecnico di Milano, 2000.) 

  26. Aizicovici, S. and McKibben, M., Existence results for a class of abstract nonlocal Cauchy problems, Nonlinear Analysis, vol 39, issue 5, Feb (2000), 649 - 668. 

  27. Aizicovici, S. and McKibben, M., Semi-linear Volterra integro-differential equations with nonlocal initial conditions, Abstract and Applied Analysis, vol 4, issue 2, (1999), 127 - 139. 

  28. McKibben, M., Nonlocal Cauchy problems for abstract functional-differential equations, (June 1999).

My current research projects are concerned with existence and stability issues of the following types of abstract equations:

-    quasilinear stochastic evolution equations

-    backward stochastic evolution equations

-    multivalued stochastic evolution equations

-    second-order impulsive evolution equations

-   stochastic evolution equations governed by fractional Brownian motion