MathSciNet:  A list of my publications appearing in MathSciNet can be found here

Google Scholar: My profile at Google Scholar can be found here

 

Preprints:

- “On bifurcation from infinity: a compactification approach”,  (with Juliana Fernandes and Phillipo Lappicy) (arxiv link)

- “Continuity of attractors of parabolic equations with nonlinear boundary conditions and rapidly varying boundaries. The case of a Lipschitz deformation”, (with Gleiciane S. Aragão and Simone M. Bruschi) (arxiv link)

 

 

ARTICLES:

77. "Homogenization in 3D thin domains with oscillating boundaries of different orders", Nonlinear Analysis TMA 251 (2025)  113667  (with Jean Carlos Nakasato and Manuel Villanueva-Pesqueira) (doi)

76. "Boundedness of solutions of nonautonomous degenerate logistic equations",  Journal of Dynamics and Differential Equations (Online First, 25 March 2024)  (with Marcos Molina-Rodríguez and Lucas A. Santos) (doi - open access)

75.  "Bifurcation and hyperbolicity for a nonlocal quasilinear parabolic problem", Advances in Differential Equations 29, numbers 1-2 (2024)  pp:1-26 (with Alexandre N. Carvalho, Estefani M. Moreira, José Valero) (doi)

74. "The p-Laplacian equation in thin domains: The unfolding approach",  Journal of Differential Equations 274  (2021) pp: 1-34 (with Jean Carlos Nakasato and Marcone C. Pereira) (doi) 

73. "Elliptic and parabolic problems in thin domains with doubly oscillatory boundary", Communications in Pure and Applied Analysis 19 (4) pp:1891-1914 (2020) (with Manuel Villanueva-Pesqueira) (doi)

72.  "Nonlinear elliptic equations with concentrating reaction terms at an oscillatory boundary", Discrete and Continuous Dynamical Systems 24 (8) pp: 4217-4246,  (2019) (with Ariadne Nogueira and Marcone C. Pereira) (doi)

71.  "Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries", Computers and Mathematics with Applications 77,  pp 536-554  (2019) (with Ariadne Nogueira and Marcone C. Pereira) (doi)

70.  "C^{1,theta}-Estimates on the distance of inertial manifolds", Collectanea Mathematica 69, pp:315-336 (2018) (with Esperanza Santamaría)  (doi)

69. "Boundary homogenization for a triharmonic intermediate problem", Mathematical Methods in Applied Science 41, Issue 3 pp 979-985 (2018) (with Francesco Ferrareso and Pier Domenico Lamberti), (doi)

68.  "Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains", Integral Equations and Operator Theory 89, Issue 3 pp 377-408 (2017) (with Francesco Ferrareso and Pier Domenico Lamberti), (doi)

67.  "Distance of attractors of reaction-diffusion equations in thin domains", Journal of Differential Equations 263, #9 pp 5459-5506 (2017) (with Esperanza Santamaría),   (doi)

66. "Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems", Journal of Differential Equations 263, #7 pp 4222-4266  (2017)  (with Pier Domenico Lamberti),  (doi)

65. "Thin domains with non-smooth oscillatory boundaries", Journal of Mathematical Analysis and Applications 446,  #1  pp. 130-164  (2017)   (with Manuel Villanueva-Pesqueira),  (doi)

64.  "Unfolding operator method for thin domains with a locally periodic highly oscillatory boundary", SIAM Journal of Mathematical Analysis  48-3,  pp. 1634-1671, (2016)  (with Manuel Villanueva-Pesqueira),  (doi)

63. "Asymptotic behavior of degenerate logistic equations", Journal of Differential Equations  259, #11 pp 6368-6398 (2015)(with R. Pardo and A. Rodríguez-Bernal), (doi)

62. "Locally periodic thin domains with varying period", C.R. Acad. Sci. Paris, Ser. I 352  pp. 397-403 (2014)   (with Manuel Villanueva-Pesqueira),  (doi)

61. "Estimates on the distance of inertial manifolds", Discrete and Continuous Dynamical Systems A 34, Vol 10 pp. 3921-3944 (2014) (with Esperanza Santamaría),   (doi)

60. "Stability estimates in $H^1_0$ for solutions of elliptic equations in varying domains", Mathematical Methods in Applied Science, 37, #2,   pp.180-186 (2014) (with Gerassimos Barbatis)

59. "Thin domains with doubly oscillatory boundary" , Mathematical Methods in Applied Science 37, #2,   pp.158-166 (2014)  (with Manuel Villanueva-Pesqueira),   (doi)

58. "Spectral stability results for higher order operators under perturbations of the domain", C. R. Acad.Sci.Paris,  Ser.I 351(2013)725–730  (with Pier D. Lamberti),  (doi)

57.  "Rate of convergence of global attractors of some perturbed reaction-diffusion problems", Topological Methods in Nonlinear Analysis 41 (2), pp. 229-253 (2013)  (with F.D.M. Bezerra and A.N. Carvalho) 

56.  "The Neumann problem in thin domains with very highly oscillatory boundaries" Journal of Mathematical Analysis and Applications 404, #1 pp  86-104  (2013) (with M.C. Pereira),  (doi)

55.  "Continuity of dynamical structures for non-autonomous evolution equations under singular perturbations", Journal of Dynamics and Differential Equations  24, #3 pp 427-481 (2012)  (with A.N. Carvalho, J.A. Langa and A. Rodríguez-Bernal), (doi)

54. "Approximating travelling waves by equilibria of non local equations" , Asymptotic Analysis 78 pp. 145-186 (2012)   (with M. López-Fernández, E. Zuazua),   (doi)

53. "On a nonlocal moving frame approximation of traveling waves,"  Comptes Rendus Mathematique  349  pp. 753-758 (2011)  (with M. López-Fernández, E. Zuazua), (doi)

52. "Homogenization in a thin domain with an oscillatory boundary"  , Journal de Mathématiques Pures et Apliquées 96, #1, pp: 29-57  (2011),  (with M.C. Pereira),  (doi)

51. "Semilinear parabolic problems in thin domains with a highly oscillatory boundary", Nonlinear Analysis: Theory, Methods and Applications 74, #15 pp: 5111-5132  (2011) (with A.N. Carvalho, M.C. Pereira, R.P. da Silva), (doi)

50. "On the supercriticality of the first Hopf bifurcation in a delay boundary problem", International Journal of Bifurcation and Chaos 20,  #9,  pp:  2955-2963   (2010) (with N. Consul and S. Oliva),  (doi) 

49.  "Infinite resonant solutions and turning points in a problem with unbounded bifurcation" , International Journal of Bifurcation and Chaos 20,  #9,  pp: 2885-2896  (2010)  (with   R. Pardo, A. Rodríguez-Bernal), (doi)

48. "Elliptic problems in thin domains with highly oscillating boundaries", Bolletin de la Sociedad Española de Matemática Aplicada 51 pp:17-24 (2010) (with M. C. Pereira)45. “Stability of the blow-up time and the blow-up set under perturbations"  , Discrete and Continuous Dynamical Systems A 26,  # 1,  pp 43-61 (2010)  (with R. Ferreira, A. de Pablo, J.D. Rossi), (doi)

47. "Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of non uniform Lispschitz deformation", Discrete and Continuous Dynamical Systems B,  Volume 14, Number 2, pp. 327–351 (2010), (with Simone M. Bruschi) (doi)

46. "Cascades of Hopf bifurcations from boundary delay", Journal of Mathematical Analysis and Applications 361, pp. 19-37 (2010) (with N. Consul and S. Oliva), (doi)

45. “Stability of the blow-up time and the blow-up set under perturbations", Discrete and Continuous Dynamical Systems A 26,  # 1,  pp 43-61 (2010)  (with R. Ferreira, A. de Pablo, J.D. Rossi),   (doi)

44. "Geometric vs. spectral convergence for the Neumann Laplacian under exterior perturbations of the domain", Integral methods in science and engineering.Volume I. Analytic Methods, pp 9-19, Birkhäuser Boston, Boston, MA, (2010)  (with David Krejcirik) 

43. "Dynamics in dumbbell domains III.  Continuity of attractors", Journal of Differential Equations, 247, pp. 225-259,  (2009)  (with A. N. Carvalho, G. Lozada-Cruz),  (doi)

42. "Dynamics in dumbbell domains II.  The limiting problem", Journal of Differential Equations 247, pp 174-202   (2009) (with A. N. Carvalho, G. Lozada-Cruz),  (doi)

41. "Equilibria and global dynamics of a problem with bifurcation from infinity", Journal of Differential Equations 246, pp. 2055-2080  (2009)  (with R. Pardo and A. Rodríguez-Bernal) (doi)

40. "The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary", Proceedings of the Royal Society of Edinburgh  138A,  223-237 (2008)   (with A. Rodríguez-Bernal and J. Rossi) (doi)

39. "Flux terms  and Robin  boundary conditions as limit of reactions and potentials concentrating in the boundary", Revista Matemática Iberoamericana,  24 nº 1, pp. 183- 211 (2008) (with A. Jiménez-Casas and A. Rodríguez-Bernal) (doi) 

38. "On the finite dimension of attractors of parabolic  problems  in $R^N$ with general potentials", Nonlinear Analysis, Theory Methods  and Applications 68, Issue 5, pp. 1082-1099 (2008)  (with N. Moya and A. Rodríguez-Bernal) (doi)

37. "On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions", Proceedings of the American Mathematical Society 136, Issue 1, pp. 151-160 (2008) (doi)

36. “Dissipative dynamics of reaction diffusion equations in R^N”, Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007), pp 405-414, (with N. Moya and A. Rodríguez-Bernal)  

35. “Robin type conditions arising from concentrated potentials”, Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 157-164 (with A. Jiménez-Casas and A. Rodríguez-Bernal)

34. “Blow up versus global boundedness of solutions of reaction diffusion equations with nonlinear boundary conditions”,Proceedings of Equadiff 11, Editors: M.Fila, A.Handlovicova, K.Mikula, M.Medved, P.Quittner and D.Sevcovic (2007). pp 1-7 (with A. Rodríguez-Bernal)

33. "Dissipative parabolic equations in locally uniform spaces", Mathematische Nachrichten 280, Issue 15. pp. 1643-1663, (2007),  (with J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal) (doi)

32. "Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lispschitz deformation", Mathematical Models and Methods in Applied Sciences, vol 17, No. 10, 1555-1585  (2007)   (with Simone M. Bruschi) (doi)

31. "Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity", Proceedings of the Royal Society of Edinburgh A,  Vol.137, Issue 02,  225-252. (2007),  (with R. Pardo and  A. Rodríguez-Bernal) (doi)

30. "Dynamics of a reaction-diffusion equation with a discontinuous nonlinearity", International Journal of Bifurcation and Chaos 16,  n. 10,  pp. 2965-2984  (2006) ,  (with A. Rodríguez-Bernal and J. Valero) (doi)

29. "Dynamics in dumbbell domains I. Continuity of the set of equilibria", Journal of Differential Equations, 231, Issue 2, pp. 551-597, (2006),   (with A.N. Carvalho and G. Lozada-Cruz) (doi)

28. "Boundary Oscillations and Nonlinear Boundary Conditions",  C. R. Acad. Sci. Paris, t. 343, Series I, pp. 99-104 (2006)  (with Simone M. Bruschi) (doi)

27.  "Problemas de valor de fronteira em domínios com oscilaçōes na fronteira", Seminario Brasileiro de Análise, Edición nº 62, Noviembre (2005),  (with Simone M. Bruschi)

26. "Nonhomogenous flux condition as limit of localized reactions'', International Conference on Differential  Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 293-295, (2005), (with A. Jiménez-Casas and A. Rodríguez-Bernal) (doi) 

25. "Ill posed problems with supercritical nonlinearities'', International Conference on Differential  Equations (EQUADIFF'03) Hasselt, Belgium. World Scientific, pp 277-280, (2005) , (with A. Rodríguez-Bernal) (doi)

24. "Non well posedness of parabolic equations with supercritical nonlinearities", Communications in Contemporary Mathematics  6,  n 5,  pp.  733-764 (2004)  (with A. Rodríguez-Bernal) (doi)

23. "Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions", Communications in Partial Differential Equations 29, 7&8, pp. 1127-1148 (2004)  (with A. Rodríguez-Bernal)  (doi)

22. "El Cálculo y la Modelización Matemática", en R. Rodríguez, E. Zuazua, De la Aritmética al Análisis: Historia y Desarrollo reciente en Matemáticas, Aulas de Verano, Instituto Superior de Formación del Profesorado, Ministerio de Educación y Ciencia, pp 11-57 (2004)

21. "Spectral Convergence and Nonlinear Dynamics for Reaction-Diffusion Equations under Perturbations of the Domain", Journal of Differential Equations 199, pp. 143-178 (2004)  (with A. Carvalho) (doi)

20. "Boundedness of Global Solutions for Nonlinear Parabolic Equations involving Gradient Blow-up Phenomena", Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. Issue 1, Volume 3/2004, Series 5,  pp 1-15,  (2004)  (with A. Rodríguez-Bernal and P. Souplet) (mathscinet review)

19.  "Linear parabolic equations in locally uniform spaces", Mathematical Models and Methods in Applied Sciences, 14, n. 2,  253-294   (2004)  (with  J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal)  (doi)

18. "Stable boundary layers in a diffusion problem with nonlinear reaction at the  boundary", Z.  angew. Math.  Phys.  55, pp. 1-14 (2004) (with N. Consul and A. Rodriguez-Bernal) (doi)

17. "Asymptotic Behavior and Attractors for Reaction Diffusion Equations in Unbounded Domains", Nonlinear Analysis, 56, pp. 515-554  (2004)  (with  J.W. Cholewa, T. Dlotko and A. Rodríguez-Bernal)  (doi)

16. "Pattern Formation from Boundary Reaction" , Fields Inst. Commun., 31, pp. 13-18, Amer. Math. Soc., Providence, RI, (2002). (with N. Consul and A. Rodriguez-Bernal) (mathscinet review)

15. "Magnetic Properties of Diruthenium (II,III)Carboxilate Compounds with Large Zero-Field Splitting and Strong Antiferromagnetic Coupling", Inorganic Chemistry,  40, 613-619,  (2001)  (with R.  Jiménez-Aparicio  and F.A.  Urbanos)

14.  "Parabolic Problems with Dynamical Boundary Condition and Singular Initial Data", Differential and Integral Equations 14, pp. 1487-1510 (2001)  (with P. Quittner and A. Rodríguez-Bernal)

13. "Spectral Behavior and Uppersemicontinuity of Attractors", International Conference on Differential  Equations (EQUADIFF'99) Berlin. World Scientific.pp 615-621 (2000).

12.  "Uppersemicontinuity of Attractors for Parabolic Problems with Localized Large Diffusion and Nonlinear Boundary Conditions", Journal of Differential Equations 168, pp 33-59 (2000). (with A. Carvalho and A. Rodríguez-Bernal)

11.  "Attractors of Parabolic Problems with Critical Nonlinearities. Uniform Bounds", Communications in Partial Differential Equations25, 1&2, pp. 1-37 (2000) (with A. Carvalho and A. Rodríguez-Bernal)

10.  "Perturbations of the Diffusion and Upper Semicontinuity of Attractors", Applied Mathematics Letters 12, pp 37-42 (1999)  (with A. Carvalho and A. Rodríguez-Bernal)

9. "Parabolic Problems with Nonlinear Boundary Conditions and Critical Nonlinearities", Journal of Differential Equations 156, pp. 376-406 (1999) (with A. Carvalho and A. Rodríguez-Bernal)

8. "Abstract Parabolic Equations with Critical Nonlinearities and Applications to Navier-Stokes and Heat Equations", Transactions of the A.M.S  352, pp. 285-310 (2000)  (with A. Carvalho)

7. "Critical Nonlinearities at the Boundary", C.R. Acad. Sci.Paris, t. 327, Série I, p. 353-358, (1998)  (with A. Carvalho and A. Rodríguez-Bernal)

6. "Domain Dependence of Elliptic Operators in Divergence Form",  Resenhas IME-USP, Vol. 3, No. 1, 107 - 123 (1997).

5.  "Elliptic Equations, Principal Eigenvalue and Dependence on the Domain", Communications in Partial Differential  Equations, 21 (5&6), 971-991 (1996)

4. "Rates of Eigenvalues on a Dummbell Domain. Simple Eigenvalue Case", Transactions of the A.M.S. Vol. 347, No. 9, (1995) 3503-3531.

3. "Neumann Eigenvalue Problems on Exterior Perturbations of the Domain", Journal of Differential Equations, Vol. 118, No. 1, (1995) 54-103

2. "A damped hyperbolic equation with critical exponent" Communications in Partial  Differential Equations17 (5 & 6), 841-866 (1992).   (with A. Carvalho and J. Hale)

1. "Eigenvalue Problems for Nonsmoothly Perturbed Domains" Journal of Differential Equations, Vol 91 (1991)  24-52  (with J. Hale and Q. Han) (doi)