PDF EndNote BibTex RIS Cite

EVOLUTION EQUATIONS IN WEIGHTED STEPANOV-LIKE PSEUDO ALMOST AUTOMORPHIC SPACES

Year 2013, Volume 3, Issue 2, 119 - 132, 01.12.2013

Abstract

In this paper, we obtain new existence and uniqueness theorem of weighted pseudo almost automorphic solutions for non-autonomous neutral partial evolution equations by applying the theory of semigroups of operators to evolution families. An interesting example is presented to illustrate our abstract result.

References

  • J. Blot, G.M. Mophou, G.M. N’Gu´er´ekata, (2009), Weighted pseudo-almost automorphic functions and applications, Nonlinear Anal., 71, 903-909.
  • S. Bochner, (1962), A new approach to almost periodicity, Proc. Nat. Acad. Sci. U.S.A., 48 , 2039-2043.
  • H.S. Ding, J. Liang, T.J. Xiao, (2009), Some prorerties of Stepanov-like almost automorphic functions and applications to abstract evolutions equations, Appl. Anal., 88 (7), 1079-1091.
  • H.S. Ding, J. Liang, T.J. Xiao, (2010), Almost automorphic mild solutions to nonautonomous semi- linear evolution equations in Banach spaces, Nonlinear Anal. TMA., 73, 1426-1438.
  • T. Diagana, (2008), Stepanov-like pseudo-almost periodicity and its applications to some nonau- tonomous differential equations, Nonlinear Anal. TMA., 69, 4277-4285.
  • T. Diagana, (2007), Stepanov-like pseudo-almost periodic functions and their applications to differ- ential equations, Commun. Math. Anal., 3 (1), 9-18.
  • T. Diagana, (2009), Existence of pseudo-almost automorphic solutions to some abstract differential equations with Sp-pseudo-almost automorphic coefficients, Nonlinear Anal. TMA., 70, 3781-3790.
  • T. Diagana, (2012), Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces, EJDE. 49, 1-19.
  • D. henry, (1981), Geometry Theory of Semilinear Parabolic Equations, Springer-verlag.
  • Z. Hu, Z. jin, (2009), Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations, Nonlinear Anal. TMA., 71, 2349-2360.
  • Z. Hu, Z. jin, (2009), Stepanov-like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with inŞnite delay, Nonlinear Anal. TMA., 71, 5381-5391.
  • Z. Hu, Z. jin, (2012), Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations, Nonlinear Anal. TMA., 75, 244-252.
  • J. Liang, J. Zhang, T.J. Xiao, (2008), Composition of pseudo-almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl., 340, 1493-1499.
  • K.J. Negel, (2000), One-Parameter Semigroups for Linear Evolution Equatons, Springer-Verlag., Vol.
  • G.M. N’Gu´er´ekata, (2005), Topics in almost automorphy, Springer-Verlag, New York.
  • G.M. N’Gu´er´ekata, A. Pankov, (2008), Stepanov-like almost automorphic functions and monotone evolution equations, Nonlinear Anal. TMA., 68, 2658-2667.
  • A. Pankov, (1990), Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equa- tions, Kluwer, Dordrecht.
  • T.J. Xiao, J. Liang, J. Zhang, (2008), Pseudo-almost automorphic solutions to semilinear differential equations in Banach space, Semigroup Forum., 76, 518-524.
  • T.J. Xiao, X.X. ZHU, J. Liang, (2009), Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. TMA., 70, 4079-4085.
  • Z. Xia, M. Fan, (2012), weighted Stepanov-like pseudo almost automorphy and applications, Nonlinear Anal. TMA., 75, 2378-2397.
  • M. Zitane, C. Bensouda, (2013), Generalized Stepanov-like pseudo almost automorphic solutions to some classes of nonautonomous evolution equations, J. Math. Comput. Sci., 3 (1), 278-303.
  • M. Zitane, C. Bensouda, (2012), Stepanov-like pseudo almost automorphic solutions to nonau- tonomous neutral partial evolution equations, Journal of Applied Mathematics & Bioinformatics., (3), 193-211.
  • M. Zitane, C. Bensouda, (2012), Weighted pseudo-almost automorphic solutions to a neutral delay integral equation of advanced type, Applied Mathemathical sciences ., 6 (122), 6087-6095.

Year 2013, Volume 3, Issue 2, 119 - 132, 01.12.2013

Abstract

References

  • J. Blot, G.M. Mophou, G.M. N’Gu´er´ekata, (2009), Weighted pseudo-almost automorphic functions and applications, Nonlinear Anal., 71, 903-909.
  • S. Bochner, (1962), A new approach to almost periodicity, Proc. Nat. Acad. Sci. U.S.A., 48 , 2039-2043.
  • H.S. Ding, J. Liang, T.J. Xiao, (2009), Some prorerties of Stepanov-like almost automorphic functions and applications to abstract evolutions equations, Appl. Anal., 88 (7), 1079-1091.
  • H.S. Ding, J. Liang, T.J. Xiao, (2010), Almost automorphic mild solutions to nonautonomous semi- linear evolution equations in Banach spaces, Nonlinear Anal. TMA., 73, 1426-1438.
  • T. Diagana, (2008), Stepanov-like pseudo-almost periodicity and its applications to some nonau- tonomous differential equations, Nonlinear Anal. TMA., 69, 4277-4285.
  • T. Diagana, (2007), Stepanov-like pseudo-almost periodic functions and their applications to differ- ential equations, Commun. Math. Anal., 3 (1), 9-18.
  • T. Diagana, (2009), Existence of pseudo-almost automorphic solutions to some abstract differential equations with Sp-pseudo-almost automorphic coefficients, Nonlinear Anal. TMA., 70, 3781-3790.
  • T. Diagana, (2012), Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces, EJDE. 49, 1-19.
  • D. henry, (1981), Geometry Theory of Semilinear Parabolic Equations, Springer-verlag.
  • Z. Hu, Z. jin, (2009), Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations, Nonlinear Anal. TMA., 71, 2349-2360.
  • Z. Hu, Z. jin, (2009), Stepanov-like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with inŞnite delay, Nonlinear Anal. TMA., 71, 5381-5391.
  • Z. Hu, Z. jin, (2012), Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations, Nonlinear Anal. TMA., 75, 244-252.
  • J. Liang, J. Zhang, T.J. Xiao, (2008), Composition of pseudo-almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl., 340, 1493-1499.
  • K.J. Negel, (2000), One-Parameter Semigroups for Linear Evolution Equatons, Springer-Verlag., Vol.
  • G.M. N’Gu´er´ekata, (2005), Topics in almost automorphy, Springer-Verlag, New York.
  • G.M. N’Gu´er´ekata, A. Pankov, (2008), Stepanov-like almost automorphic functions and monotone evolution equations, Nonlinear Anal. TMA., 68, 2658-2667.
  • A. Pankov, (1990), Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equa- tions, Kluwer, Dordrecht.
  • T.J. Xiao, J. Liang, J. Zhang, (2008), Pseudo-almost automorphic solutions to semilinear differential equations in Banach space, Semigroup Forum., 76, 518-524.
  • T.J. Xiao, X.X. ZHU, J. Liang, (2009), Pseudo-almost automorphic mild solutions to nonautonomous differential equations and applications, Nonlinear Anal. TMA., 70, 4079-4085.
  • Z. Xia, M. Fan, (2012), weighted Stepanov-like pseudo almost automorphy and applications, Nonlinear Anal. TMA., 75, 2378-2397.
  • M. Zitane, C. Bensouda, (2013), Generalized Stepanov-like pseudo almost automorphic solutions to some classes of nonautonomous evolution equations, J. Math. Comput. Sci., 3 (1), 278-303.
  • M. Zitane, C. Bensouda, (2012), Stepanov-like pseudo almost automorphic solutions to nonau- tonomous neutral partial evolution equations, Journal of Applied Mathematics & Bioinformatics., (3), 193-211.
  • M. Zitane, C. Bensouda, (2012), Weighted pseudo-almost automorphic solutions to a neutral delay integral equation of advanced type, Applied Mathemathical sciences ., 6 (122), 6087-6095.

Details

Primary Language English
Journal Section Research Article
Authors

Charaf BENSOUDA This is me
Universit´e Ibn Tofa¨ıl, Facult´e des Sciences, D´epartement de Math´ematiques, Laboratoire d’An. Maths et GNC, B.P. 133, K´enitra 1400, Maroc.


Mohamed ZİTANE This is me
Universit´e Ibn Tofa¨ıl, Facult´e des Sciences, D´epartement de Math´ematiques, Laboratoire d’An. Maths et GNC, B.P. 133, K´enitra 1400, Maroc

Publication Date December 1, 2013
Published in Issue Year 2013, Volume 3, Issue 2

Cite

Bibtex @ { twmsjaem761403, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {2}, pages = {119 - 132}, title = {EVOLUTION EQUATIONS IN WEIGHTED STEPANOV-LIKE PSEUDO ALMOST AUTOMORPHIC SPACES}, key = {cite}, author = {Bensouda, Charaf and Zitane, Mohamed} }