Evolution Equations, Dispersive estimates, Difference Equations, Fractional Differential Equation

Master Degree Students (work concluded)

(1) Bruno de Andrade
1. Equac¸˜oes de evolu¸c˜ao Discretas de Segunda Orden: Regularidade Maximal e Teoria de Perturba¸ca˜o , 2008.
Federal University of Pernambuco. Brazil.

(2) Arlu´cio da Cruz Viana
1. Dicotomia exponencial para equac¸˜oes funcionais discretas com retardo in?nito, 2009. Federal University of Pernambuco. Brazil.

(3) Giovana Siracusa Gouveia
1. Um estudo do comportamento assinto´tico para equa¸c˜oes em diferenc¸a com retardo in?nito, 2009.
Federal University of Pernambuco. Brazil.

Ph.D. Students (Thesis direction concluded)

(1) Luis del Campo
1. “Asymptotic Theory for Retarded Functional Di?erence Equations”, PH.D. The- sis 2003, Federal University of Pernambuco, Brazil.
2. “An Asymptotic Theory for Retarded Functional Di?erence Equations”, Compu- ter & Mathematics with Applications, Pergamon-Elsevier, Oxford, UK, v. 49, p. 841-855, 2005.
3. Asymptotic Expansion for Di?erence Equation with In?nite Delay, Asian- European Journal of Mathematics, World Scienti?c, v. 2 (1),19-40, 2009.

(2) Airton Castro
1. Well-posedness of second order evolution equation on discrete time and applica- tions, PHD Thesis 2009, Federal University of Pernambuco, Brazil.
2. Maximal regularity of the Discrete Harmonic Oscillator Equation. Advances In Di?erence Equations, Hindawi Publ. Corp. NY, USA, vol. 2009, Article ID 290625, 1-14, 2009.
3. Well-posedness of Second Order Evolution Equation on discrete time, Journal of Di?erence Equations and Applications, Taylor & Francis, London, UK, 2010, 1-14.
4. Perturbation Theory, Stability, Boundedness and Asymptotic Behavior for Second Order Evolution Equation in discrete time.
Journal of Difference Equations and Applications, Taylor & Francis, London, UK, 2011, 327-358.

(3) Julio Cesar de Souza
1. A regularity theory for certain evolution equations in discrete and continuous time scale, PH.D. Thesis 2009, Federal University of Pernambuco, Brazil.
2. S-Asymptotically w-periodic solutions of semilinear fractional integro-differential equations, Applied Mathematics Letters, Elsevier-USA, 22, 2009, 865-870.
3. A perturbation theory for the Discrete Harmonic Oscillator Equation. Journal of Di?erence Equations and Applications, Taylor & Francis, London, UK, (16)(2) 2010, 1413-1428.
4. Existence of S-Asymptotically w-periodic solutions for fractional order functio- nal Integro-Differential Equations with infinite delay. Elsevier-USA,
Nonlinear Analysis Series A: Theory, Methods and Applications, 72(2010), 1683-1689.
5. The complex inversion formula for k-convoluted semigroup, Applicable Analysis, 91 (15) (2012), 937-946.

(4) Bruno de Andrade
1. A periodicity theory for certain evolution equations, PHD Thesis 2010, Federal University of Pernambuco, Brazil.
2. Almost automorphic and pseudo-almost automorphic solutions to semilinear evo- lution equations with nondense domain,
Journal of Inequalities and Applicati-ons, Hindawi Publ. Corp. NY, USA, vol. 2009, Article ID 2982207, 1-8, doi:10.1155/2009/298207, 2009.
3. Compact almost automorphic solutions to semilinear Cauchy problems with non- dense domain, Applied Mathematics and Computation, 215 (2009), 2843-2849.
4. S-asymptotically ?-periodic and asymptotically ?-periodic solutions to semilinear Cauchy problems with non dense domain, Elsevier-USA,
Nonlinear Analysis Series A: Theory, Methods and Applications, 72(2010), 3190-3208.
5. Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations,
Nonlinear Analysis Series B: Real World Applications, (11) 2010, 3532-3554.
6. ”On type of periodicity and ergodicity to a class of fractional order di?erential equations,
”Advances in Di?erence Equations, Hindawi Publ. Corp. NY, USA, Vol. 2010, Article ID 179750, 1-25.
7. ”On type of periodicity and ergodicity to a class of integral equations with in?nite delay”,
Journal of Nonlinear and Convex Analysis, (11)(2), 309-335, 2010.

(5) Alejandro Caicedo
1. “Asymptotic behavior for functional equations with in?nite delay”, PHD Thesis 2011, Federal University of Pernambuco, Brazil.
2. “S-asymptotically ?-periodic solutions of abstract partial neutral integro- differential equations”,
Functional Differential Equations. vol. 17 (1-2), 2010, 387-405.
3. “Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces”,
Journal of the Franklin Institute Vol. 349 (2012), 1-24, Doi:10.1016/j.jfranklin.2011.02.001.
4. Stabilization of distributed control systems with delay, Systems & Con- trol Letters, Elsevier, The Netherlands,
Vol. 60(9)(2011), 675-682, doi:10.1016/j.sysconle.2011.04.012.
5. Asymptotic periodicity for a class of partial integro-di?erential equations,
ISRN Mathematical Analysis, Volume 2011 (2011), Article ID 537890, 18 pages doi:10.5402/2011/537890.
6. “Asymptotically periodic solutions of neutral partial differential equations with infinite delay”,
Communications on Pure and Applied Analysis,
American Insti tute of Mathematical Sciences (AIMS), Volume 12, Number 5, September 2013, pp. 2031-2068, doi:10.3934/cpaa.2013.12.

(6) Alex Sepulveda
1. Generalized forms of periodicity for fractional and integral di?erential equations, PHD Thesis 2012, Universidad de La Frontera, Chile.
2. Weighted S-asymptotically w-periodic solutions of a class of fractional di?eren- tial equations,
Advances in Di?erence Equations, Volume 2011, Article ID 584874, 13 pages, doi:10.1155/2011/584874.
3. “Almost periodic and pseudo-almost periodic solutions to fractional di?erential and integro-di?erential equations”,
Applied Mathematics and Computation 218 (2011), 1735-1745. doi:10.1016/j.amc.2011.06.054.
4. “Pseudo almost automorphic solutions to fractional di?erential and integro- di?erential equations”,
Communications in Applied Analysis, Dynamic Pu- blishers, Inc., 16 (1) (2012), 131-152.

(7) Erwin Henr´?quez
1. Asymptotic periodicity for a class of partial integro-di?erential equations, PHD Thesis 2012, Universidad de La Frontera, Chile.
2. “Asymptotic periodicity for some classes of integro-di?erential equations and ap- plications”,
Advances in Mathematical Sciences and Applications, Volume 21 (1) (2011), 1-31, Gakkotosho Co., Tokyo, Japan.
3. “Almost automorphic solutions of hyperbolic evolution equations”,
Banach Jour nal of Mathematical Analysis, Vol.06 (1) (2012), 90-100.
4. “Asymptotic periodicity and almost automorphy for a class of Volterra integro- di?erential equations”,
Mathematical Methods in the Applied Sciences, John Wi- ley & Sons, v. 35 (2012), 795-811, DOI: 10.1002/mma.1607.

(8) Filipe Dantas
1. About the behavior of Volterra di?erence equations, PHD Thesis 2013, Federal University of Pernambuco, Brazil.
2. “Almost automorphic pro?le of solutions for di?erence equations of Volterra type”,
Journal of Applied Mathematics and Computing, Springer-Verlag, 42 (2013),1-18, DOI 10.1007/s12190-012-0615-3.
3. “lp-boundedness properties for Volterra di?erence equations”,
Applied Mathema-tics and Computation, Elsevier-USA, Volume 219, Issue 12, 15 February 2013, 6986-6999, DOI 10.1016/j.amc.2012.12.053.
4. “About the behavior of solutions for Volterra di?erence equations with in?nite delay”,
Journal of Computational and Applied Mathematics, Elsevier, 255 (2014), 44-59, Doi 10.1016/j.cam.2013.04.033.

Ph.D. Student (Thesis direction in advance)

(1) Mario Choquehuanca
1. Boundedness properties and asymptotic behavior of Volterra di?erence equations, PHD Thesis 2012, University of La Frontera, Chile.
2. “lp-boundedness properties for Volterra di?erence equations”,
Applied Mathema- tics and Computation, Elsevier-USA, Volume 219, Issue 12, 15 February 2013, 6986-6999, DOI 10.1016/j.amc.2012.12.053.
3. “Asymptotic analysis for Volterra di?erence equations”,
Asymptotic Analysis, IOS PRESS, The Netherlands, Volume 88 (3) (2014), 125-164.

(2) Clessius Silva UFPE 2013

(4) Filipe Andrade UFPE 2014

Postdoctoral Student (work concluded)

(1) Miguel Frasson, PhD. Universidade de Leiden, The Netherlands, 01/01/2011- 31/12/2011.
1. “Semilinear functional di?erence equations with in?nite delay”, Mathematical and Computer Modeling, Elsevier, v. 55, No 3-4, pp. 1083-1105, 2012.
2. “Asymptotic behavior of solutions to linear neutral delay di?erential equations with periodic coe?cients”, Preprin