Toka Diagana, Ph.D.
Department of Mathematics
Washington DC 20059
My personal web page
Ph. D. (1999) Université Claude Bernard - Lyon, France
- Evolution Equations
- Operator Theory
- Functional Analysis
- Stochastic Differential Equations
- Difference Equations
- Integro-differential Equations
- P-adic Spectral Theory
I am interested in the study of the stability, the existence and
uniqueness of (periodic, almost periodic, almost automorphic, pseudo-almost periodic, pseudo-almost
automorphic) solutions to degenerate differential equations, fractional differential equations,
difference equations, integro-differential equations, and stochastic differential equations as well
as their applications to practical problems.
I am also interested in a general spectral theory for unbounded linear operators in the p-adic setting.
- Almost automorphic type and almost periodic type functions in abstract spaces, Springer, New York, 2013
- (with P. H. Bezandry) Almost Periodic Stochastic Processes, Springer, New York, 2011, 235 pp.
- (with F. Ramaroson)Spectral Theory for Finite Rank Perturbations of Unbounded Diagonal Operators in Non-Archimedean Hilbert Space.Contemporary Mathematics (American Math. Society.--2015(In Press).
- (With Aymen Ammar and Aref Jeribi) Perturbations of Fredholm Linear Relations in Banach Spaces with Application to 3x3 Block Matrices of Linear Relations.Arab Journal of Mathematical Sciences--2015(In Press).
- Perturbations of Unbounded Fredholm Linear Operators in Banach Spaces.Handbook in Operator Theory, Springer, pp. 1--5, 2014.
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients. Math. Slovaca 65(2015), no.1, 121-140.
- (with R. Kerby, T. H. Miabey, and F. Ramaroson)Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space.P-Adic Numbers Ultrametric Anal.6 (2014), no. 3, pp. 171-187.
- Almost automorphic solutions to a Beverton-Holt dynamic equation with survival rate. Appl. Math. Lett. 36 (2014), pp. 19-24.
- Existence of pseudo almost automorphic mild solutions to some nonautonomous second order differential equations. Rocky Mt. J. Math. 43 (2013), No. 3, 793-824.
- (with P. H. Bezandry) Square-Mean Almost Periodic Solutions to Some Classes of Nonautonomous Stochastic Evolution Equations With Finite Delay. J. Appl. Funct. Anal. 7 (2012), no. 4, 345--366.
- Almost periodic solutions to some second-order nonautonomous differential equations. Proc. Amer. Math. Soc. 140 (2012), no. 1, 279--289.
- Pseudo-almost periodic solutions for some classes of nonautonomous partial evolutions equations. J. Franklin Inst. 348 (2011), no. 8, 2082 -- 2098.
- Almost periodic solutions for some higher-order nonautonomous differential equations with operator coefficients. Math. Comput. Modeling 54 (2011), no. 11-12, 2672 -- 2685.
- Almost automorphic mild solutions to some classes of nonautonomous higher-order differential equations. Semigroup Forum 82 (2011), no. 3, pp. 455-477.
- Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations. J. Math. Anal. Appl. 350 (2009), no. 1, 18--28.
- (with M. Baroun, S. Boulite, and L. Maniar), Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations. J. Math. Anal. Appl. 349 (2009), no. 1, 74--84.
- (with H. Henriquez and E. Hernandez), Asymptotically almost periodic solutions to some classes of second-order functional differential equations. Differential Integral Equations 21 (2008), no. 5-6, 575--600.
- (with P. H. Bezandry and S. Elaydi), On the stochastic Beverton-Holt equation with survival rates. J. Difference Equ. Appl. 14 (2008), no. 2, pp. 175-190.
I serve in the editorial board of several mathematical journals including the following:
- Communications in Mathematical Analysis (CMA)
- Journal of Abstract Differential Equations and Applications (JADEA)
- African Diaspora Journal Of Mathematics (ADJM)