Periodic solutions of degenerate differential equations in vector-valued function spaces

Studia Mathematica

Volumn 202, Issue 1, 2011, Pages 49-63

  Lizama, Carlos ^a   Ponce, Rodrigo ^a  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Besov spaces; Degenerate parabolic equations; Operator valued Fourier multipliers; R boundedness; UMD spaces

Indexed keywords

EID: 79958797645     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm202-1-3     Document Type: Article

References (30)

1. H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces and applications, Math. Nachr. 186 (1997), 5-56. (Pubitemid 127343855)
2. -, Linear and Quasilinear Parabolic Problems. Volume I: Abstract Linear Theory, Monogr. Math. 89, Birkhäuser, Basel, 1995.
3. W. Arendt and S. Bu, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Math. Z. 240 (2002), 311-343. (Pubitemid 36195202)
4. -, -, Operator-valued Fourier multiplier on periodic Besov spaces and applications, Proc. Edinburgh Math. Soc. 47 (2004), 15-33.
5. V. Barbu and A. Favini, Periodic problems for degenerate differential equations, Rend. Inst. Mat. Univ. Trieste 28 (1997), Suppl., 29-57.
6. J. Bourgain, Some remarks on Banach spaces in which martingale differences sequences are unconditional, Ark. Mat. 21 (1983), 163-168.
7. S. Bu and Y. Fang, Maximal regularity of second order delay equations in Banach spaces, Sci. China Math. 53 (2010), 51-62.
8. -, -, Periodic solutions of delay equations in Besov spaces and Triebel-Lizorkin spaces, Taiwanese J. Math. 13 (2009), 1063-1076.
9. -, -, Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces, Studia Math. 184 (2008), 103-119.
10. S. Bu and J. Kim, Operator-valued Fourier multipliers on periodic Triebel spaces, Acta Math. Sinica (Engl. Ser.) 21 (2005), 1049-1056. (Pubitemid 41502335)
11. D. L. Burkholder, A geometrical condition that implies the existence of certain singular integrals on Banach-space-valued functions, in: Proc. Conference on Harmonic Analysis in Honor of Antoni Zygmund (Chicago, 1981), Wadsworth, Belmont, CA, 1983, 270-286.
12. P. L. Butzer and H. Berens, Semi-groups of Operators and Approximation, Grundlehren Math. Wiss. 145, Springer, 1967.
13. R. W. Carroll and R. E. Showalter, Singular and Degenerate Cauchy Problems, Math. Sei. Engrg. 127, Academic Press, New York, 1976.
14. R. Denk, M. Hieber and J. Prüss, R-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Mem. Amer. Math. Soc. 166 (2003), no. 788.
15. A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution equations, Ann. Mat. Pura Appl. 163 (1993), 353-394.
16. -, -, Space and time regularity for degenerate evolution equations, J. Math. Soc. Japan 44 (1992), 331-350.
17. -, -, Degenerate Differential Equations in Banach Spaces, Pure Appl. Math. 215, Dekker, New York, 1999.
18. A. Favini and G. Marinoschi, Periodic behaviour for a degenerate fast diffusion equation, J. Math. Anal. Appl. 351 (2009), 509-521.
19. M. Girardi and L. Weis, Criteria for R-boundedness of operator families, in: Lecture Notes in Pure Appl. Math. 234, Dekker, New York, 2003, 203-221.
20. -, -, Operator-valued Fourier multiplier theorems on Besov spaces, Math. Nachr. 251 (2003), 34-51.
21. A. Haraux, Nonlinear Evolution Equations-Global Behavior of Solutions, Lecture Notes in Math. 841, Springer, 1981.
22. V. Keyantuo and C. Lizama, Fourier multipliers and integro-differential equations in Banach spaces, J. London Math. Soc. 69 (2004), 737-750. (Pubitemid 38845768)
23. -, -, Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces, Studia Math. 168 (2005), 25-50.
24. V. Keyantuo, C. Lizama and V. Poblete, Periodic solutions of integro-differential equations in vector-valued function spaces, J. Differential Equations 246 (2009), 1007-1037.
25. C. Lizama, Fourier multipliers and periodic solutions of delay equations in Banach spaces, J. Math. Anal. Appl. 324 (2006), 921-933. (Pubitemid 44524543)
26. C. Lizama and V. Poblete, Maximal regularity for perturbed integral equations on periodic Lebesgue spaces, J. Math. Anal. Appl. 348 (2008), 775-786.
27. G. Marinoschi, Functional Approach to Nonlinear Models of Water Flow in Soils, Math. Model. Theory Appl. 21, Springer, Dordrecht, 2006.
28. -, Periodic solutions to fast diffusion equations with non-Lipschitz convective terms, Nonlinear Anal. Real World Appl. 10 (2009), 1048-1067.
29. V. Poblete, Solutions of second-order integro-differential equations on periodic Besov spaces, Proc. Edinburgh Math. Soc. 50 (2007), 477-492.
30. H.-J. Schmeisser and H. Triebel, Topics in Fourier Analysis and Function Spaces, Wiley, Chichester, 1987.