μ-Pseudo compact almost automorphic weak solutions for some partial functional differential inclusions

References

• Biroli M. Sur les solutions bornées et presque périodiques des équations et inéquations d'évolution. Ann Mat Pura Appl. 1972;93:1–79.
   Google Scholar
• Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Amsterdam, London: North-Holland; 1973.
   Google Scholar
• Haraux A. Comportement à l'infini pour certains systèmes dissipatifs non linéaires. Proc Roy Soc Edinburgh Sect A. 1979;84(3-4):213–234.
   Google Scholar
• Haraux A. Nonlinear evolution equations-Global behavior of solutions. Berlin Heidelberg, New-York,: Springer Verlag; 1981. (Lecture Notes in Mathematics; 841).
   Google Scholar
• Haraux A. Asymptotic behavior of two-dimensional quasi-autonomous almost periodic evolutions equations. J Differ Equ. 1987;66(1):62–70.
   Web of Science ®Google Scholar
• Ishii H. On the existence of almost periodic trajectories for contractive almost periodic processes. J Differ Equ. 1982;43(1):66–72.
   Web of Science ®Google Scholar
• Wexler D. Nonlinear passive evolution equations. J Differ Equ. 1977;23(3):414–435.
   Web of Science ®Google Scholar
• Es-sebbar B, Ezzinbi K, Fatajou S, et al. Compact almost automorphic weak solutions for some monotone differential inclusions: applications to parabolic and hyperbolic equations. J Math Anal Appl. 2020;486(1):123805.
   Google Scholar
• Bochner S. Beiträge zur theorie der fastperiodischen funktionen. Math Ann. 1927;96(1):119–147.
   Google Scholar
• Stepanov W. Sur quelques généralisations des fonctions presque périodiques. C R Acad Sci Paris. 1925;181(20):90–94.
   Google Scholar
• Stepanov W. Über einige verallgemeinerungen der fastperiodischen funktionen. Math Ann. 1926;95(1):473–498.
   Google Scholar
• Zhang C. Pseudo almost periodic functions and their applications [thesis]. The University of Western Ontario; 1992.
   Google Scholar
• Diagana T. Weighted pseudo almost periodic functions and applications. C R Math Acad Sci Paris. 2006;343(10):643–646.
   Google Scholar
• Diagana T, Mophou GM, N'Guérékata GM. Existence of weighted pseudo almost periodic solutions to some classes of differential equations with Sp-weighted pseudo almost periodic coefficients. Nonlinear Anal. 2010;72(1):430–438.
   Web of Science ®Google Scholar
• Bochner S. Curvature and Betti numbers in real and complex vector bundles. Univ E Politec Torino Rend Sem Mat. 1955;15:225–253.
   Google Scholar
• Liang J, Zhang J, Xiao TJ. Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl. 2008;340(2):1493–1499.
   Web of Science ®Google Scholar
• Xiao TJ, Liang J, Zhang J. Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. Semigroup Forum. 2008;76(3):518–524.
   Web of Science ®Google Scholar
• Blot J, Mophou GM, N'guérékata GM, et al. Weighted pseudo almost automorphic functions and applications to abstract differential equations. Nonlinear Anal. 2009;71(3-4):903–909.
   Web of Science ®Google Scholar
• Blot J, Cieutat P, Ezzinbi K. New approach for weighted pseudo almost periodic functions under the light of measure theory, basic results and applications. Appl Anal. 2011;92(3):1–34.
   Web of Science ®Google Scholar
• Blot J, Cieutat P, Ezzinbi K. Measure theory and pseudo almost automorphic functions: new developments and applications. Nonlinear Anal. 2012;75(4):2426–2447.
   Web of Science ®Google Scholar
• Ezzinbi K, Toure H, Zabsonre I. Weighted Pseudo almost periodic and Pseudo almost automorphic solutions of class r for some partial differential equations. Differ Equ Dyn Syst. 2018;29:1–26.
   Google Scholar
• Zheng ZM, Ding HS. On completeness of the space of weighted pseudo almost automorphic functions. J Funct Anal. 2015;268(10):3211–3218.
   Web of Science ®Google Scholar
• Liu JH, Song XQ. Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations. J Funt Anal. 2010;258(1):196–207.
   Web of Science ®Google Scholar
• Dunkl CF, Williams KS. A simple norm inequality. Amer Math Monthly. 1964;71(1):53–54.
   Web of Science ®Google Scholar
• Blot J, Cieutat P. Completeness of sums of subspaces of bounded functions and applications. Commun Math Anal. 2018;19(2):43–61.
   Google Scholar
• Rudin W. Real and complex analysis. 3rd ed. New-York: McGraw-Hill Book Compagny; 1986.
   Google Scholar
• Corduneanu C. Almost periodic functions. New York: Wiley; 1968. (Reprented, Chelsea, New York, 1989)
   Google Scholar
• Corduneanu C. Almost periodic oscillations and waves. Springer Science and Business Media, Now York; 2009.
   Google Scholar
• Tarallo M. A Stepanov version for Favard theory. Arch Math. 2008;90(1):53–59.
   Web of Science ®Google Scholar
• Amerio L, Prouse G. Almost periodic functions and functional equations. Van Nostrand Reinhold, New York; 1971.
   Google Scholar
• Bochner S. Abstrakte fastperiodische funktionen. Acta Mathematica. 1933;61(1):149–184.
   Google Scholar
• Es-sebbar B, Ezzinbi K. Stepanov ergodic perturbations for some neutral partial functional differential equations. Math Meth Appl Sci. 2016;39(8):1945–1963.
   Web of Science ®Google Scholar
• Akdad AN, Ezzinbi K, Souden L. Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations. Nonauton Dyn Syst. 2015;2:12–30.
   Google Scholar
• Diagana T, Herniquez HR, Hernández EM. Almost automorphic mild solutions to some partial neutral functional differential equations and applications. Nonlinear Anal. 2008;69(5–6):1485–1493.
   Web of Science ®Google Scholar
• Fink A. Extensions of almost automorphic sequences. J Math Anal Appl. 1969;27(1):519–523.
   Google Scholar
• Veech WA. Almost automorphic functions on groups. Amer J Math. 1965;87(3):719–751.
   Google Scholar
• Diagana T. Stepanov-like pseudo almost periodicity and its applications to some nonautonomous differential equations. Nonlinear Anal. 2008;69(12):4277–4285.
   Web of Science ®Google Scholar
• Jendoubi C. μ-Pseudo almost periodic solutions for delayed partial functional differential equations in admissible spaces. Appl Anal. 2019;25:1–19.
   Google Scholar
• Rockafellar RT. On the maximal monotonicity of subdifferential mappings. Pacific J Math. 1970;33(1):209–216.
   Web of Science ®Google Scholar