Existence Results for Integro-Differential Equations with Reflection

References

• Adivar, M., Koyuncuoǧlu, H. C. (2016). Almost automorphic solutions of discrete delayed neutral system. J. Math. Anal. Appl. 435(1):532–550.
   Web of Science ®Google Scholar
• Baskakov, A., Obukhovskii, V., Zecca, P. (2018). Almost periodic solutions at infinity of differential equations and inclusions. J. Math. Anal. Appl. 462(1):747–763. DOI: 10.1016/j.jmaa.2018.02.034.
   Web of Science ®Google Scholar
• Bochner, S. (1964). Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. Sci. USA 52:907–910. DOI: 10.1073/pnas.52.4.907.
   PubMed Web of Science ®Google Scholar
• N’Guérékata, G. M. (2001). Almost Automorphic and Almost Periodic Functions in Abstract Spaces. New York: Kluwer Academic Plenum Publishers.
   Google Scholar
• Papageorgiou, N. S., Rădulescu, V. D., Repovš, D. D. (2018). Periodic solutions for a class of evolution inclusions. Comput. Math. Appl. 75(8):3047–3065. DOI: 10.1016/j.camwa.2018.01.031.
   Web of Science ®Google Scholar
• Papageorgiou, N. S., Rădulescu, V. D., Repovš, D. D. (2019). Periodic solutions for implicit evolution inclusions. Evol. Equation Control Theory. 8(3):621–631. DOI: 10.3934/eect.2019029.
   Google Scholar
• Ait Dads, E., Ezzinbi, K., Miraoui, M. (2015). (μ,ν)−Pseudo almost automorphic solutions for some nonautonomous differential equations. Int. J. Math. 26:1–21.
   Web of Science ®Google Scholar
• Ait Dads, E., Fatajou, S., Khachimi, L. (2012). Pseudo almost automorphic solutions for differential equations involving reflection of the argument. Int. Scholarly Res. Network ISRN Math. Anal. 2012:1–20. DOI: 10.5402/2012/626490.
   Google Scholar
• Ait Dads, E., Khelifi, S., Miraoui, M. (2020). On the integro-differential equations with reflection. Math. Meth. Appl. Sci. 43(17):10262–10275. DOI: 10.1002/mma.6693.
   Web of Science ®Google Scholar
• Ben-Salah, M., Miraoui, M., Rebey, A. (2019). New results for some neutral partial functional differential equations. Results Math. 74(4):181. . (2019). DOI: 10.1007/s00025-019-1106-8.
   Web of Science ®Google Scholar
• Blot, J., Cieutat, P., Ezzinbi, K. (2012). Measure theory and pseudo almost automorphic functions: new developments and applications. Nonlinear Anal. 75(4):2426–2447. DOI: 10.1016/j.na.2011.10.041.
   Web of Science ®Google Scholar
• Chérif, F., Miraoui, M. (2019). New results for a Lasota-Wazewska model. Int. J. Biomath. 12(2):1950019. DOI: 10.1142/S1793524519500190.
   Web of Science ®Google Scholar
• Diagana, T., Ezzinbi, K., Miraoui, M. (2014). Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory. Cubo . 16(2):01–31. DOI: 10.4067/S0719-06462014000200001.
   Google Scholar
• Li, K. X. (2015). Weighted pseudo almost automorphic solutions for nonautonomous SPDEs driven by Levy noise. J. Math. Anal. Appl. 427(2):686–721. DOI: 10.1016/j.jmaa.2015.02.071.
   Web of Science ®Google Scholar
• Miraoui, M. (2017). Existence of μ−pseudo almost periodic solutions to some evolution equations. Math. Methods Appl. Sci. 40(13):4716–4726.
   Web of Science ®Google Scholar
• Miraoui, M. (2017). Pseudo almost automorphic solutions for some differential equations with reflection of the argument. Numer. Funct. Anal. Optim. 38(3):376–394. DOI: 10.1080/01630563.2017.1279175.
   Web of Science ®Google Scholar
• Miraoui, M., Ezzinbi, K., Rebey, A. (2017). μ−Pseudo almost periodic solutions in α−norm to some neutral partial differential equations with finite delay. Dyn. Contin. Discrete Impulsive Syst. Canada 24(1):83–96.
   Google Scholar
• Miraoui, M., Yaakoubi, N. (2019). Measure pseudo almost periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Numer. Funct. Anal. Optim. 40(5):571–585. DOI: 10.1080/01630563.2018.1561469.
   Web of Science ®Google Scholar
• Zhang, C. (1994). Pseudo almost periodic solutions of some differential equations. J. Math. Anal. Appl. 181(1):62–76. DOI: 10.1006/jmaa.1994.1005.
   Web of Science ®Google Scholar
• Kong, F., Nieto, J. J. (2019). Almost periodic dynamical behaviors of the hematopoiesis model with mixed discontinuous harvesting terms. Discrete Contin. Dyn. Syst. B 24(11):5803–5830.
   Web of Science ®Google Scholar
• Diagana, T. (2005). Pseudo almost periodic solutions to some differential equations. Nonlinear Anal. 60(7):1277–1286. DOI: 10.1016/j.na.2004.11.002.
   Web of Science ®Google Scholar
• Gupta, C. P. (1987). Existence and uniqueness theorem for boundary value problems involving reflection of the argument. Nonlinear Anal.: TheoryMethods Appl. 11(9):1075–1083. DOI: 10.1016/0362-546X(87)90085-X.
   Web of Science ®Google Scholar
• Sharkovskii, A. N. (1978). Functional-differential equations with a finite group of argument transformations in asymptotic behavior of solutions of functional-differential equations. Akad. Nauk Ukrain., Inst. Math. Kiev. 157:118–142.
   Google Scholar
• Aftabizadeh, A. R., Huang, Y. K., Wiener, J. (1988). Bounded solutions for differential equations with reflection of the argument. J. Math. Anal. Appl. 135(1):31–37. DOI: 10.1016/0022-247X(88)90139-4.
   Web of Science ®Google Scholar
• Aftabizadeh, A. R., Wiener, J. (1985). Boundary value problems for differential equations with reflection of argument. Int. J. Math. Math. Sci. 8(1):151–163. DOI: 10.1155/S016117128500014X.
   Google Scholar
• Gupta, C. P. (1987). Two point boundary value problems involving reflection of the argument. Int. J. Math. Math. Sci. 10(2):361–371. DOI: 10.1155/S0161171287000425.
   Google Scholar
• Piao, D. (2004). Periodic and almost periodic solutions for differential equations with reflection of the argument. Nonlinear Anal.: Theory Methods Appl. 57(4):633–637. DOI: 10.1016/j.na.2004.03.017.
   Web of Science ®Google Scholar
• Piao, D. (2004). Pseudo almost periodic solutions for differential equations involving reflection of the argument. J. Korean Math. Soc. 41(4):747–754. DOI: 10.4134/JKMS.2004.41.4.747.
   Web of Science ®Google Scholar
• Miraoui, M. (2020). Measure pseudo almost periodic solutions for differential equations with reflection. Appl. Anal. DOI: 10.1080/00036811.2020.1766026.
   Web of Science ®Google Scholar
• Xin, N., Piao, D. (2012). Weighted pseudo almost periodic solutions for differential equations involving reflection of the argument. Int. J. Phys. Sci. 7(11):1806–1810.
   Google Scholar