# Rodrigo Ponce C.

Assistant Professor at the Instituto de Matemática y Física, Universidad de Talca, Chile.

## Research and Publications

### Publications:

1. Periodic solutions of degenerate differential equations in vector-valued function spaces, Joint work with C. Lizama. Studia Math., 202 (2011), 49-63. More
2. Bounded solutions to a class of semilinear integro-differential equations in Banach spaces, Joint work with C. Lizama. Nonlinear Anal., 74 (2011) 3397-3406. More
3. Almost automorphic solutions to abstract Volterra equations on the line, Joint work with C. Lizama. Nonlinear Anal., 74 (2011) 3805-3814. More
4. Maximal Regularity for Perturbed Integral Equations on the Line, Joint work with C. Lizama. Integral Equations Operator Theory 74 (2012), no. 4, 513-526. More
5. Bounded mild solutions to fractional integro-differential equations in Banach spaces, Semigroup Forum, 87, (2013), 377-392, DOI 10.1007/s00233-013-9474-y. More
6. Hölder continuous solutions for fractional differential equations and maximal regularity, J. of Differential Equations, 255 (2013), 3284-3304. More
7. Maximal regularity for degenerate differential equations with infinite delay in periodic vector-valued function spaces, Joint work with C. Lizama. Proc. Edin. Math. Soc. 56 (2013), no. 3, 853-871. More
8. Hölder continuous solutions for Sobolev type differential equations, Math. Nachr. 287, No. 1, 70-78 (2014), DOI 10.1002/mana.201200168. More
9. A connection between almost periodic functions defined on time scales and R, with C. Lizama and J. G. Mesquita. Appl. Anal., (2014), DOI 10.1080/00036811.2013.875161. More
10. On the boundedness of generalized Cèsaro operators on Sobolev spaces, Joint work with C. Lizama, P.J. Miana and L. Sánchez-LaJusticia. J. Math. Anal. Appl. 419 (2014), no. 1, 373-394. More
11. On $C^\alpha$-Hölder classical solutions for non-autonomous neutral differential equations: the nonlinear case, Joint work with E. Hernández and D. O'Regan. J. Math. Anal. Appl. 420 (2014), no. 2, 1814-1831. More
12. Weighted pseudo almost automorphic solutions to a semilinear fractional differential equation with Stepanov-like weighted pseudo almost automorphic nonlinear term, Joint work with Y. K. Chang and Mei-Juan Zhang. Applied Math. and Computation, 257 (2015) 158-168. More
13. Weighted pseudo antiperiodic solutions for fractional integro-differential equations in Banach spaces, Joint work with E. Álvarez and C. Lizama. Applied Math. and Computation, 259 (2015) 164-172. More
14. On the compactness of fractional resolvent families, Joint work with C. Lizama and A. Pereira. Semigroup Forum, (2016), DOI 10.1007/s00233-016-9788-7. More
15. Existence of mild solutions to nonlocal fractional Cauchy problems via compactness, Abstract and applied analysis, (2016), Article ID 4567092. More
16. Maximal $L^p$-regularity for fractional differential equations on the line. Joint work with V. Poblete. Math. Narch. 290, No. 13, 2009-2023 (2017), DOI 10.1002/mana.201600175. More
17. On the well-posedness of degenerate fractional differential equations in vector valued function spaces, Israel J. of Math. 219, (2017) 727-755. More
18. Almost automorphic solutions of Volterra equations on time scales. Joint work with C. Lizama, with J.G. Mesquita and E. Toon, Differential and Integral Equations, 30 (2017), 667-694. More
19. Approximate controllability for fractional differential equations of Sobolev type via properties on resolvent operators. Joint work with Y. K. Chang and A. Pereira. Fractional calculus and applied analysis, 20, (2017), 963-987. More
20. Discrete-time theorems for global and pointwise dichotomies of cocycles over semiflows. Joint work with F. Bataran and C. Preda. Monatshefte fur Mathematik, 186 (2018), no. 4, 579-607. More
21. Well-posedness, regularity, and asymptotic behavior of the continuous and discrete solutions of linear fractional integro-differential equations with order varying in time. Joint work with E. Cuesta. Electronic J. of Differential Equations, Vol. 2018, 173, (2018), 1-27. More
22. Uniform exponential stability and its applications to bounded solutions of integro-differential equations in Banach spaces. Joint work with Y. K. Chang. J. Integral Equations and applications, 30 (2018), no. 3, 347-369. More
23. Existence and optimal controls for fractional stochastic evolution equations of Sobolev type via fractional resolvent operators. Joint work with Y. K. Chang and Y. Pei. Journal of Optimization Theory and Applications, 2018, Article in Press. https://doi.org/10.1007/s10957-018-1314-5. More
24. Sobolev type time fractional differential equations and optimal controls with the order in $(1,2).$ Joint work with Y. K. Chang. Differential and Integral Equations, 2018, to appear. More
25. Bounded solutions to functional integro-differential equations arising from heat conduction in materials with memory. Joint work with J. Alzabut and Y. K. Chang. Journal of Mathematical Sciences, 2018, to appear. More
26. Norm continuity for strongly continuous families of operators. Joint work with C. Lizama and A. Pereira. International Journal of Evolution Equations 10, (2017), 145-162. More
27. Asymptotic behavior and uniform integrability of the generalized Mittag-Leffler function and its applications to Fractional differential equations.
28. Existence of solutions for abstract nonlinear fractional differential equations. Joint work with D. O'Regan and E. Hernández. Submitted.
29. Mild solutions of fractional differential inclusions with nonlocal initial conditions via resolvent family of operators. Joint work with Y. K. Chang and X. Yang. Submitted.
30. Properties of solution sets for Sobolev type fractional differential inclusions via resolvent family of operators. Joint work with Y. K. Chang and X. Yang. Submitted.
31. Asymptotic behavior and representation of solutions to a Volterra kind of equation with a singular kernel. Joint work with M. Warma. Submitted.
32. Asymptotic behavior of Sobolev type resolvents and its applications to fractional differential equations. Joint work with S. Rueda. Submitted.
33. Abstract cosine and sine functions on time scales and applications to abstract Cauchy problems. Joint work with J. G. Mesquita and A. Pereira. Submitted.
34. Recurrence of bounded solutions for a functional integro-differential equation arising from heat conduction in materials with memory. Joint work with Y. K. Chang. and J. Alzabut. Submitted.

### Projects:

Fondecyt Grant 11130619: Stability of resolvent families and applications

## Teaching and Students

Calculus I, II, III, Ordinary differential equations, and other related topics in undergraduate programs.

Analysis I, II, III, IV, Fourier Analysis, Functional Analysis I and II in Math graduate program.