Semi-Bloch periodic functions, semi-anti-periodic functions and applications
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 245-255.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce the notions of semi-Bloch periodic functions and semi-anti-periodic functions. Stepanov semi-Bloch periodic functions and Stepanov semi-anti-periodic functions are considered, as well. We analyze the invariance of introduced classes under the actions of convolution products and briefly explain how one can use the obtained results in the qualitative analysis of solutions of abstract inhomogeneous integro-differential equations.
Keywords: semi-Bloch $k$-periodic functions, semi-anti-periodic functions, integro-differential equations.
@article{CHFMJ_2020_5_2_a4,
     author = {B. Chaouchi and M. Kosti\'c and S. Pilipovi\'c and D. Velinov},
     title = {Semi-Bloch periodic functions, semi-anti-periodic functions and applications},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {245--255},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a4/}
}
TY  - JOUR
AU  - B. Chaouchi
AU  - M. Kostić
AU  - S. Pilipović
AU  - D. Velinov
TI  - Semi-Bloch periodic functions, semi-anti-periodic functions and applications
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2020
SP  - 245
EP  - 255
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a4/
LA  - ru
ID  - CHFMJ_2020_5_2_a4
ER  - 
%0 Journal Article
%A B. Chaouchi
%A M. Kostić
%A S. Pilipović
%A D. Velinov
%T Semi-Bloch periodic functions, semi-anti-periodic functions and applications
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2020
%P 245-255
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a4/
%G ru
%F CHFMJ_2020_5_2_a4
B. Chaouchi; M. Kostić; S. Pilipović; D. Velinov. Semi-Bloch periodic functions, semi-anti-periodic functions and applications. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 245-255. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a4/

[1] Hasler M.F., Guérékata G.M.N'., “Bloch-periodic functions and some applications”, Nonlinear Studies, 21 (2014), 21–30 | MR | Zbl

[2] Hasler M.F., “Bloch-periodic generalized functions”, Novi Sad Journal of Mathematics, 46 (2016), 135–143 | MR | Zbl

[3] Kostić M., Velinov D., “Asymptotically Bloch-periodic solutions of abstract fractional nonlinear differential inclusions with piecewise constant argument”, Funct. Anal. Appr. Comp., 9 (2017), 27–36 | MR | Zbl

[4] Chen Y.Q., “Anti-periodic solutions for semilinear evolution equations”, Journal of Mathematical Analysis and Applications, 315 (2006), 337–348 | MR | Zbl

[5] Guérékata G.M.N'., Valmorin V., “Antiperiodic solutions of semilinear integrodifferential equations on a Banach space”, Applied Mathematics and Computation, 2018 (2012), 11118–11124 | MR

[6] Liu J.H., Song X.Q., Zhang L.T., “Existence of anti-periodic mild solutions to semilinear nonautonomous evolution equations”, Journal of Mathematical Analysis and Applications, 425 (2015), 295–306 | MR | Zbl

[7] Dimbour W., Valmorin V., “Asymptotically antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space”, Applied Mathematics and Computation, 7 (2016), 1726–1733 | MR

[8] Liu J., Zhang L., “Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain”, SpringerPlus, 5 (2016), 704

[9] Kostić M., Velinov D., “A note on almost anti-periodic functions in Banach spaces”, Kragujevac Journal of Mathematics, 44 (2020), 287–297

[10] Andres J., Pennequin D., “Semi-periodic solutions of difference and differential equations”, Boundary Value Problems, 141 (2012), 1–16 | MR

[11] Andres J., Pennequin D., “Limit-periodic solutions of difference and differential systems without global Lipschitzianity restricitons”, Journal of Difference Equations and Applications, 24 (2018), 955–975 | MR | Zbl

[12] Bart H., Goldberg S., “Characterizations of almost periodic strongly continuous groups and semigroups”, Mathematische Annalen, 236 (1978), 105–116 | MR | Zbl

[13] Besicovitch A.S., Almost Periodic Functions, Dover Publ., New York, 1954, 180 pp. | MR

[14] Guérékata G.M.N'., Almost Automorphic and Almost Periodic Functions in Abstract Spaces, Kluwer Academic Publ., Dordecht, 2001 | MR | Zbl

[15] Diagana T., Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces., Springer, Cham, Heidelberg, New York, 2013, 302 pp. | MR | Zbl

[16] Kostić M., Almost Periodic and Almost Automorphic Type Solutions of Abstract Volterra Integro-Differential Equations, Walter de Gruyter, Berlin, Berlin, Boston, 2019, 329 pp. | MR

[17] Bohr H., Følner E., “On some types of functional spaces: A contribution to the theory of almost periodic functions”, Acta Mathematica, 76 (1944), 31–155 | MR

[18] Kostić M., “Existence of generalized almost periodic and asymptotic almost periodic solutions to abstract Volterra integro-differential equations”, Electronic Journa of Differential Equations, 2017:239 (2017), 1–30 | MR