RESEARCH

Domains of interests

Qualitative properties of solutions to some PDE
Stabilization

Publications
1. Strong stabilization of damped nonlinear Schrödinger equation with saturation on unbounded domains, J. Math. Anal. Appl., 538 (2024), no. 1, Paper No. 128329, with Jesús Ildefonso Díaz
2. Finite time extinction for a critically damped Schrödinger equation with a sublinear nonlinearity, Adv. Differential Equations, 28 (2023), no. 3-4, 311-340, with Jesús Ildefonso Díaz
3. The dual space of a complex Banach space restricted to the field of real numbers, Adv. Math. Sci. Appl., 31 (2022), no. 2, 241-252
4. Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity, J. Differ. Equations, 308 (2022), 252-285, with Jesús Ildefonso Díaz
5. On a Stationary Schrödinger Equation with Periodic Magnetic Potential, RACSAM, 115 (2021), paper no. 72, 1-32, with Ian Schindler
6. Finite time extinction for a damped nonlinear Schrödinger equation in the whole space, Electron. J. Differential Equations, 2020 (2020), no. 39, 1-18
7. Finite time extinction for the strongly damped nonlinear Schrödinger equation in bounded domains, J. Differ. Equations, 268 (2020), no. 7, 4029-4058, with Jesús Ildefonso Díaz
8. On damped second-order gradient systems, J. Differ. Equations, 259 (2015), no. 7, 3115-3143 & no. 8, 4412, with Jérôme Bolte and Mohamed Ali Jendoubi
9. Existence of weak solutions to some stationary Schrödinger equations with singular nonlinearity, RACSAM, 109 (2015), 43-63, with Jesús Ildefonso Díaz
10. A sharper energy method for the localization of the support to some stationary Schrödinger equations with a singular nonlinearity, Discrete Contin. Dyn. Syst. Series A, 34 (2014), no. 9, 3371-3382, with Jesús Ildefonso Díaz
11. Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations, Electron. J. Differential Equations, 2014 (2014), no. 90, 1-15, with Jesús Ildefonso Díaz
12. Localizing estimates of the support of solutions of some nonlinear Schrödinger equations - The stationary case, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29 (2012), no. 1, 35-58, with Jesús Ildefonso Díaz
13. A generalized interpolation inequality and its application to the stabilization of damped equations, J. Differ. Equations, 240 (2007), no. 2, 324-356, with Fernando Soria
14. Mass concentration phenomena for the L²-critical nonlinear Schrödinger equation, Trans. Am. Math. Soc., 359 (2007), no. 11, 5257-5282, with Ana Vargas
15. On a nonlinear Schrödinger equation with a localizing effect, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 459-463, with Jesús Ildefonso Díaz
16. Maximum decay rate for finite-energy solutions of nonlinear Schrödinger equations, Differential Integral Equations, 17 (2004), no. 11-12, 1411-1422
17. Maximum decay rate for the nonlinear Schrödinger equation, NoDEA Nonlinear Differential Equations and Applications, 11 (2004), no. 4, 451-467
18. Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation, Adv. Math. Sci. Appl., 12 (2002), no. 2, 817-827
19. Convergence to scattering states in the nonlinear Schrödinger equation, Commun. Contemp. Math., 3 (2001), no. 3, 403-418