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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 4
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Research Article

Pseudo-almost periodic C0 solutions to the evolution equations with nonlocal initial conditions

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Pages 1027-1037 | Received 16 Nov 2020, Accepted 29 Jul 2021, Published online: 23 Aug 2021

References

  • I. I. Vrabie. Almost periodic solutions for nonlinear delay evolutions with nonlocal initial conditions. J Evol Equ. 2013;13(3):693–714.
  • I. I. Vrabie. Existence for nonlinear evolution inclusions with nonlocal retarded initial conditions. Nonlinear Anal Theory Methods Appl. 2011;7418:7047–7060.
  • I. I. Vrabie. Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions. J Funct Anal. 2012;262(4):1363–1391.
  • I. I. Vrabie. Global solutions for nonlinear delay evolution inclusions with nonlocal initial conditions. Set Val Variat Anal. 2012;20(1):477–497.
  • Burlică M, Roşu D. A class of nonlinear delay evolution equations with nonlocal initial conditions. Proc Am Math Soc. 2014;142(7):2445–2458.
  • Meknani B. The existence and uniqueness of integral solutions to some nonlinear reaction–diffusion system with nonlocal retarded initial conditions. J Taibah Univ Sci. 2020 Jan;14(1):569–578. DOI:org/10.1080.
  • Lizama C, Alvarez-Pardo E. Pseudo asymptotic solutions of fractional order semilinear equations. Banach J Math Anal. 2013;7(2):42–52.
  • Alvarez-Pardo E, Lizama C. Weighted pseudo almost periodic solutions to a class of semilinear integro-differential equations in banach spaces. Adv Differ Equ. 2015;2015(1):1–18.
  • García-Falset J, Reich S. Integral solutions to a class of nonlocal evolution equations. Commun Contemp Math. 2010;12(6):1031–1054.
  • Paicu A, Vrabie II. A class of nonlinear evolution equations subjected to nonlocal initial conditions. Nonlinear Anal Theory Methods Appl. 2010;72(11):4091–4100.
  • Deng K. Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions. J Math Anal Appl. 1993;179:630–637.
  • McKibben M. Discovering evolution equations with applications: Volume 2-stochastic equations. New York (NY): Chapman and Hall/CRC; 2011.
  • Zhang CY. Pseudo almost periodic solutions of some differential equations. J Math Anal Appl. 1994;181(1):62–76.
  • Zhang CY. Pseudo almost periodic solutions of some differential equations ii. J Math Anal Appl. 1995;192(2):543–561.
  • Zhang CY. Integration of vector-valued pseudo-almost periodic functions. Proc Am Math Soc. 1994;121(1):167–174.
  • Diagana T. Pseudo almost periodic functions in banach spaces. New York (NY): Nova Science Publishers Inc.; 2007.
  • Diagana T, Hernández EM. Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional–differential equations and applications. J Math Anal Appl. 2007;327(2):776–791.
  • Diagana T, N'Guérékata G. Pseudo almost periodic mild solutions to hyperbolic evolution equations in intermediate banach spaces. Appl Anal. 2006;85(6–7):769–780.
  • Cuevas C, Hernández E. Pseudo-almost periodic solutions for abstract partial functional differential equations. Appl Math Lett. 2009;22(4):534–538.
  • Cuevas C, Sepulveda A, Soto H. Almost periodic and pseudo-almost periodic solutions to fractional differential and integro-differential equations. Appl Math Comput. 2011;218(5):1735–1745.
  • Agarwal RP, Cuevas C, Soto H. Pseudo-almost periodic solutions of a class of semilinear fractional differential equations. J Appl Math Comput. 2011;37(1-2):625–634.
  • Pinto M. Pseudo-almost periodic solutions of neutral integral and differential equations with applications. Nonlinear Anal Theory Methods Appl. 2010;72(12):4377–4383.
  • Ezzinbi K, Fatajou S, N'Guérékata GM. Pseudo almost automorphic solutions for dissipative differential equations in banach spaces. J Math Anal Appl. 2009;35(12):765–772.
  • Yu Y, Gong S. Pseudo-almost periodic solutions for first-order neutral differential equations. Adv Differ Equ. 2018;2018(1):114.
  • Ding HS, Ji MX. Pseudo-almost periodic solutions for a discrete nicholson's blowflies model with harvesting term. Adv Differ Equ. 2016;2016(1):289.
  • Hale J. Theory of functional differential equations. 2nd ed. Vol. 3, Applied mathematical sciences. New York (NY): Springer-Verlag; 1977.
  • Hale JK, Lunel SMV. Introduction to functional differential equations. 1st ed. Vol. 99, Applied mathematical sciences. New York (NY): Springer; 2013.
  • Kolmanovskii V, Myshkis A. Introduction to the theory and applications of of functional differential equations. Vol. 463, Mathematics and its applications. Dordrecht: Kluwer Academic Publishers; 1999.
  • Ahmed NU. Semigroup theory with applications to systems and control. Vol. 246, Pitman research notes in mathematics series. Harlow: Longman Scientific & Technical; 1991.
  • Diagana T. Almost automorphic type and almost periodic type functions in abstract spaces. New York (NY): Springer; 2013.
  • Engel KJ, Nagel R. One-parameter semigroups for linear evolution equations. Semigroup Forum. 2001;63:278–280.
  • Kamenskii MI, Obukhovskii VV, Zecca P. Condensing multivalued maps and semilinear differential inclusions in banach spaces. Vol. 7, De Gruyter series in nonlinear analysis and applications. Berlin: Walter de Gruyter; 2001.
  • Pazy A. Semigroups of linear operators and applications to partial differential equations. Vol. 44, Applied mathematical sciences. New York (NY): Springer-Verlag; 1983.
  • Wu J. Theory and applications of partial functional differential equations. Vol. 119, Applied mathematical sciences. New York (NY): Springer; 1996.
  • Zheng S. Nonlinear evolution equations. New York (NY): Chapman and Hall/CRC; 2004.
  • Perestiuk NA, Plotnikov VA, Skripnik NV, et al. Differential equations with impulse effects: multivalued right-hand sides with discontinuities. Berlin: Walter de Gruyter; 2011.
  • Baghli S, Benchohra M. Uniqueness results for partial functional differential equations in fréchet spaces. Fixed Point Theory. 2008;9(2):395–406.
  • Benchohra M, Medjadj I. Global existence results for functional differential inclusions with delay. J Math Sci. 2015;5(208):477–486.
  • Barbu V. Nonlinear differential equations of monotone type in banach spaces. Springer monographs in Mathematics. New York (NY): Springer-Verlag; 2010.
  • Vrabie II. Compactness methods for nonlinear evolutions. 2nd ed. Vol. 75, Pitman monographs and surveys in pure and applied mathematics. Harlow: Longman; 1995.
  • Vrabie II. Nonlinear retarded evolution equations with nonlocal initial conditions. Dyn Syst Appl. 2012;21(2–3):417–439.

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