Weighted $S^p$-pseudo $S$-asymptotically periodic solutions for some systems of nonlinear delay integral equations with superlinear perturbation
Ural mathematical journal, Tome 9 (2023) no. 1, pp. 78-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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This work is concerned with the existence of positive weighted pseudo $S$-asymptotically periodic solution in Stepanov-like sense for some systems of nonlinear delay integral equations. In this context, we will first be interested in establishing a suitable composition theorem, and then some existing results concerning the $S$-asymptotic periodicity in the scalar case are developed here for the vector case. We point out that, in this paper, we adopt some changes in the definitions, which, although slight, are necessary to accomplish the work.
Keywords: weighted $S^{p}$-pseudo $S$-asymptotic periodicity, $S$-asymptotic periodicity, systems of nonlinear delay integral equations, equations with superlinear perturbation.
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     title = {Weighted $S^p$-pseudo $S$-asymptotically periodic solutions for some systems of nonlinear delay integral equations with superlinear perturbation},
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Hamza El Bazi; Abdellatif Sadrati. Weighted $S^p$-pseudo $S$-asymptotically periodic solutions for some systems of nonlinear delay integral equations with superlinear perturbation. Ural mathematical journal, Tome 9 (2023) no. 1, pp. 78-92. http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a5/

[1] Blot J., Cieutat P., N'Guérékata G. M., “$S$-asymptotically $\omega$-periodic functions and applications to evolution equations”, Afr. Diaspora J. Math., 12:2 (2011), 113–121 | MR | Zbl

[2] Blot J., Mophou G. M., N'Guérékata G. M., Pennequin D., “Weighted pseudo almost automorphic functions and applications to abstract differential equations”, Nonlinear Anal., 71 (2009), 903–909 | DOI | MR | Zbl

[3] Brezis H., Functional Analysis, Sobolev Spaces and Partial Differential Equations, 1st, NY, 2010, 600 pp. | DOI | MR

[4] Cooke K. L., Kaplan J. L., “A periodicity threshold theorem for epidemics and population growth”, Math. Biosci., 31:1–2 (1976), 87–104 | DOI | MR | Zbl

[5] Cuevas C., de Souza J. C., “$S$-asymptotically $\omega$-periodic solutions of semilinear fractional integro-differential equations”, Appl. Math. Lett., 22:6 (2009), 865–870 | DOI | MR | Zbl

[6] Diagana T., Mophou G. M., N'Guérékata G. M., “Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with $S^{p}$-weighted pseudo-almost periodic coefficients”, Nonlinear Anal., 72:1 (2010), 430–438 | DOI | MR | Zbl

[7] Dimbour W., Mado J.-C., “$S$-asymptotically $\omega$-periodic solution for a nonlinear differential equation with piecewise constant argument in a Banach space”, CUBO. Math. J., 16:3 (2014), 55–65 URL: https://hal.science/hal-02067049 | MR | Zbl

[8] Dimbour W., Manou-Abi S. M., “Asymptotically $\omega$-periodic functions in the Stepanov sense and its application for an advanced differential equation with piecewise constant argument in a Banach space”, Mediterr. J. Math., 15 (2018), 25 | DOI | MR | Zbl

[9] He B., Wang Q.-R., Cao J.-F., “Weighted $S^{p}$-pseudo $S$-asymptotic periodicity and applications to Volterra integral equations”, Appl. Math. Comput., 380 (2020), 125–275 | DOI | MR

[10] Henríquez H. R., Pierri M., Táboas P., “On $S$-asymptotically $\omega$-periodic functions on Banach spaces and applications”, J. Math. Anal. Appl., 343 (2008), 1119–1130 | DOI | MR | Zbl

[11] Lee H. M., Jang H. H., Yun C. M., “$S$-asymptotically $\omega$-periodic mild solutions for the systems of differential equations with piecewise constant argument in Banach spaces”, J. Chungcheong Math. Soc., 31:1 (2018), 13–27 | DOI | MR | Zbl

[12] N'Guérékata G. M., Pankov A., “Stepanov-like almost automorphic functions and monotone evolution equations”, Nonlinear Anal., 68:9 (2008), 2658–2667 | DOI | MR | Zbl

[13] Sadrati A., Zertiti A., “A study of systems of nonlinear delay integral equations by using the method of upper and lower solutions”, Int. J. Math. Comput., 17:4 (2012), 93–102 | MR

[14] Sadrati A., Zertiti A., “A topological methods for Existence and multiplicity of positive solutions for some systems of nonlinear delay integral equations”, Int. J. Math. Stat., 13:1 (2013), 47–55 | MR | Zbl

[15] Sadrati A., Zertiti A., “Existence and uniqueness of positive almost periodic solution for systems of nonlinear delay integral equations”, Electron. J. Diff. Equ., 2015:116 (2015), 1–12 | MR

[16] Sadrati A., Zertiti A., “The Existence and uniqueness of positive weighted pseudo almost automorphic solution for some systems of neutral nonlinear delay integral equations”, Int. J. Appl. Math., 29:3 (2016), 331–347 | DOI | MR | Zbl

[17] Xia Z. N., “Weighted pseudo asymptotically periodic mild solutions of evolution equations”, Acta. Math. Sin.-English Ser., 31:8 (2015), 1215–1232 | DOI | MR | Zbl

[18] Zhao J.-Y., Ding H.-S., N'Guérékata G. M., “$S$-asymptotically periodic solutions for an epidemic model with superlinear perturbation”, Adv. Differ. Equ., 2016 (2016), 221 | DOI | MR