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Tytuł artykułu

Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
online
2015-07-07
Twórcy
  • Département de Mathématiques, Université Cadi Ayyad, Faculté des Sciences B.P. 2390 Marrakech, Morocco
  • Département de Mathématiques, Université Cadi Ayyad, Faculté des Sciences B.P. 2390 Marrakech, Morocco
autor
  • Département de Mathématiques, Faculté Des Sciences De Gafsa, Cité Zarroug 2121, Gafsa, Tunisie
Bibliografia
  • [1] C. Zhang, Integration of vector-valued pseudo-almost periodic functions, Proc. Am. Math. Soc. 121(1), (1994), 167-174.
  • [2] C.Y. Zhang, Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl. 151, (1994), 62-76.
  • [3] C.Y. Zhang, Pseudo almost periodic solutions of some differential equations II, J. Math. Anal. Appl. 192, (1995), 543-561.
  • [4] C. Corduneanu, Almost Periodic Functions, Wiley, New York, 1968.
  • [5] S. Bochner; Continuous mappings of almost automorphic and almost periodic functions, Proc. Nat. Acad. Sci. USA, 52, (1964), 907-910. [Crossref]
  • [6] H.X. Li, L.L. Li, Stepanov-like pseudo almost periodicity and semilinear differential equations with uniform continuity, Reaults. Math. 59, (2011), 43-61. [WoS]
  • [7] J. Blot, G.M. Mophou, G.M. NGuérékata and D. Pennequin, Weighted pseudo almost automorphic functions and applications to abstract differential equations, Nonlinear Analysis, Theory, Methods and Applications Vol 71, Issue 3-4, (2009), 903-909.
  • [8] J. Blot, P. Cieutat and K. Ezzinbi: New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications Applicable Analysis, (2011), 1-34.
  • [9] J. Blot, P. Cieutat and K. Ezzinbi: Measure theory and pseudo almost automorphic functions, new developements and applications Applicable Analysis, (2011), 1-29. [WoS]
  • [10] M. Damak, K. Ezzinbi and L. Souden, Weighted pseudo-almost periodic solutions for some neutral partial functional differential equations, Vol. 2012, No. 47, (2012), 1-13.
  • [11] M. Frechet, Sur le théorème ergodique de Birkhoff, C. R. Math. Acad. Sci. Paris 213, (1941), 607-609 (in French).
  • [12] L.Maniar, R. Schnaubelt, Almost periodicity of inhomogeneous parabolic evolution equations , in: Lecture Notes in Pure and Appl. Math. vol. 234, Dekker, New york, 2003, 299-318.
  • [13] T.Diagana: Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations. J. Math. Anal. Appl. 350, (2009), 18-28.
  • [14] J. Liang, T.J. Xiao, J. Zhang, Decomposition of weighted pseudo almost periodic functions, Nonlinear Anal. 73, (10), (2010), 3456-3461.
  • [15] T.Diagana: Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations Nonlinear Analysis. 69, (2008), 4277-4285.
  • [16] T. Diagana, Giséle M. Mophou and Gaston M. N’Guérékata: Existence of weighted pseudo almost periodic solutions to some classes of differential equations with Sp-weighted pseudo almost periodic coefficients Nonlinear Analysis. 72, (2010), 430- 438.
  • [17] T. Diagana: stepanov -like pseudo almost periodicity and its application to some nonautonomes differential equation, Commun. Math. Anal.3, (2007), 9-18.
  • [18] T. Diagana: Weighted pseudo almost periodic functions and applications C.R.A.S, 343, (10), (2006), 643-646.
  • [19] T. Diagana: Existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations Nonlinear Analysis. 74, (2011), 600-615.
  • [20] T. Diagana: Weighted pseudo-almost periodic solutions to some differential equations Nonlinear Analysis. 68, (2008), 2250- 2260.
  • [21] T. Diagana, Existence of p-almost automorphic mild solution to some abstract differential equations, Int. J. Evol. Equ. 1, (2005), 57-67.
  • [22] T.J. Xiao, J. Liang, J. Zhang, Pseudo almost automorphic solution to semilinear differential equations in Banach spaces, Semigroup Forum 76, (2008), 518–524. [WoS][Crossref]
  • [23] H. Lee and H. Alkahby, Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay, Nonlinear Anal. 69, (2008), 2158-2166.
  • [24] K. Ezzinbi, S. Fatajou, G.M. N’Guérékata, Pseudo almost automorphic solutions to some neutral partial functional differential equations in Banach spaces, Nonlinear Anal. TMA 70, (2009), 1641-1647.
  • [25] G.M. N’Guérékata, Topics in Almost Automorphy, Springer-Verlag, New York, 2005.
  • [26] P. Acquistapace, B. Terreni, A unified approach to abstract linear parabolic equations, Rend. Sem. Mat. Univ. Padova. 78, (1987), 47-107.
  • [27] G.M. N’Guérékata, A. Pankov, Stepanov-like almost automorphic functions and monotone evolution equations, Nonlinear Analysis. TMA, 68, (2008), 2658-2667. [Crossref]
  • [28] R. P. Agarwal, Bruno de Andrade and Claudio Cuevas,Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations Nonlinear Analysis: RealWorld Applications. 11, (2010), 3532-3554.
  • [29] Z.R. Hu, Z. Jin, Stepanov-like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay, Nonlinear Anal. 71, (2009), 5381-5391.
  • [30] K.J. Engel, R. Nagel, one parametr semigroups for linear evolution equations, in: Graduate texts in Mathematics, Springer- Verlag, 2000.
  • [31] M. Baroun, S. Boulite, G. M. N’Guérékata, L. Maniar, Almost automorphy of semilinear parabolic evolution equations, Electronic Journal of Differential Equations, No. 60 (2008), 1–9.
  • [32] Z. Hu, Z. Jin Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations Nonlinear Analysis, 75, (2012), 244-252.
  • [33] Z. Hu, Z. Jin Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations Nonlinear Analysis, 71, (2009), 2349-2360.
  • [34] H. S. Dinga, J. Lianga, G. M. N’Guérékatab, T. J. Xiao Pseudo almost periodicity of some nonautonomous evolution equations with delay Nonlinear Analysis, 67, (2007), 1412-1418.
  • [35] H. Lee, H. Alkahby Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay Nonlinear Analysis, 69, (2008), 2158-2166.
  • [36] T.J. Xiao, X.X. Zhu, J. Liang, Pseudo almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. TMA 70 (2009), 4079-4085.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_msds-2015-0002
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