Positive periodic solutions for certain kinds of delayed q-difference equations with biological background
Tóm tắt
This paper specifically focuses on a specific type of q-difference equations that incorporate multiple delays. The main objective is to explore the existence of positive periodic solutions using coincidence degree theory. Notably, the equation studied in this paper has relevance to important biological growth models constructed on quantum domains. The significance of this research lies in the fact that quantum domains are not translation invariant. By investigating periodic solutions on quantum domains, the paper introduces a new perspective and makes notable advancements in the related literature, which predominantly focuses on translation invariant domains. This research contributes to a better understanding of periodic dynamics in systems governed by q-difference equations with multiple delays, particularly in the context of biological growth models on quantum domains.
Tài liệu tham khảo
citation_journal_title=Math. Slovaca; citation_title=A new periodicity concept for time scales; citation_author=M Adıvar; citation_volume=63; citation_issue=4; citation_publication_date=2013; citation_pages=817-828; citation_doi=10.2478/s12175-013-0127-0; citation_id=CR1
citation_journal_title=Appl. Math. Comput.; citation_title=Floquet theory based on new periodicity concept for hybrid systems involving
-difference equations; citation_author=M Adıvar, HC Koyuncuoğlu; citation_volume=273; citation_publication_date=2016; citation_pages=1208-1233; citation_doi=10.1016/j.amc.2015.08.124; citation_id=CR2
citation_journal_title=Comput. Math. Appl.; citation_title=Stability and periodicity in dynamic delay equations; citation_author=M Adıvar, Y Raffoul; citation_volume=58; citation_issue=2; citation_publication_date=2009; citation_pages=264-272; citation_doi=10.1016/j.camwa.2009.03.065; citation_id=CR3
citation_journal_title=Math. Methods Appl. Sci.; citation_title=
-asymptotically periodic functions, first-order Cauchy problem, and Lasota-Wazewska model with unbounded oscillating production of red cells; citation_author=E Alvarez, S Castillo, M Pinto; citation_volume=43; citation_issue=1; citation_publication_date=2020; citation_pages=305-319; citation_doi=10.1002/mma.5880; citation_id=CR4
citation_journal_title=Differ. Equ. Adv.; citation_title=On the existence and uniqueness of
-periodic solutions to a class of Volterra difference equations; citation_author=E Alvarez, S Diaz, C Lizama; citation_publication_date=2019; citation_doi=10.1186/s13662-019-2053-0; citation_id=CR5
citation_journal_title=Electron. J. Qual. Theory Differ. Equ.; citation_title=
-periodic functions and mild solutions to abstract fractional integro-differential equations; citation_author=E Alvarez, A Gomez, M Pinto; citation_volume=2018; citation_issue=16; citation_publication_date=2018; citation_pages=1-8; citation_doi=10.14232/ejqtde.2018.1.16; citation_id=CR6
citation_journal_title=Sarajev. J. Math.; citation_title=Floquet theory for
-difference equations; citation_author=M Bohner, R Chieochan; citation_volume=8; citation_issue=2; citation_publication_date=2012; citation_pages=1-12; citation_doi=10.5644/SJM.08.2.14; citation_id=CR7
citation_journal_title=J. Appl. Funct. Anal.; citation_title=Positive periodic solutions for higher-order functional
-difference equations; citation_author=M Bohner, R Chieochan; citation_volume=8; citation_issue=1; citation_publication_date=2013; citation_pages=14-22; citation_id=CR8
citation_journal_title=J. Biol. Dyn.; citation_title=The Beverton-Holt
-difference equation; citation_author=M Bohner, R Chieochan; citation_volume=7; citation_issue=1; citation_publication_date=2013; citation_pages=86-95; citation_doi=10.1080/17513758.2013.804599; citation_id=CR9
citation_journal_title=J. Math. Anal. Appl.; citation_title=Periodic averaging principle in quantum calculus; citation_author=M Bohner, JG Mesquita; citation_volume=435; citation_issue=2; citation_publication_date=2016; citation_pages=1146-1159; citation_doi=10.1016/j.jmaa.2015.10.078; citation_id=CR10
citation_journal_title=Proc. Am. Math. Soc.; citation_title=Massera’s theorem in quantum calculus; citation_author=M Bohner, JG Mesquita; citation_volume=146; citation_issue=11; citation_publication_date=2018; citation_pages=4755-4766; citation_doi=10.1090/proc/14116; citation_id=CR11
citation_journal_title=Math. Morav.; citation_title=Optimal harvesting policy for the Beverton-Holt quantum difference model; citation_author=M Bohner, S Streipert; citation_volume=20; citation_issue=2; citation_publication_date=2016; citation_pages=39-57; citation_doi=10.5937/MatMor1602039B; citation_id=CR12
citation_journal_title=Opusc. Math.; citation_title=The second Cushing-Henson conjecture for the Beverton-Holt
-difference equation; citation_author=M Bohner, S Streipert; citation_volume=37; citation_issue=6; citation_publication_date=2017; citation_pages=795-819; citation_doi=10.7494/OpMath.2017.37.6.795; citation_id=CR13
citation_journal_title=J. Comp. Appl. Math.; citation_title=Second order
-difference equations solvable by factorization method; citation_author=A Dobrogowska, A Odzijewicz; citation_volume=193; citation_issue=1; citation_publication_date=2006; citation_pages=319-346; citation_doi=10.1016/j.cam.2005.06.009; citation_id=CR14
Gaines, R.E., Mahwin, J.L.: Coincidence Degree, and Nonlinear Differential Equations, in: Lecture Notes in Mathematics. Springer, Heidelberg (2006). doi:10.1007/BFb0089537
citation_journal_title=Adv. Dyn. Syst. Appl.; citation_title=Existence of periodic solutions for a quantum Volterra equation; citation_author=M Islam, JT Neugebauer; citation_volume=11; citation_issue=1; citation_publication_date=2016; citation_pages=67-80; citation_id=CR16
citation_journal_title=Sarajev. J. Math.; citation_title=Asymptotically
-periodic solutions of a quantum Volterra integral equation; citation_author=M Islam, JT Neugebauer; citation_volume=14; citation_issue=1; citation_publication_date=2018; citation_pages=59-70; citation_doi=10.5644/SJM.14.1.06; citation_id=CR17
citation_journal_title=Comput. Math. Appl.; citation_title=Existence of positive periodic solutions for a class of difference equations with several deviating arguments; citation_author=D Jiang, RP Agarwal; citation_volume=45; citation_issue=6–9; citation_publication_date=2003; citation_pages=1303-1309; citation_doi=10.1016/S0898-1221(03)00103-2; citation_id=CR18
Kac, V., Cheung, P.: Quantum Calculus. Springer, New York (2012). doi:10.1007/978-1-4613-0071-7
citation_journal_title=J. Math. Anal. Appl.; citation_title=Periodic solutions for a neutral nonlinear dynamical equation on a time scale; citation_author=ER Kaufmann, Y Raffoul; citation_volume=319; citation_issue=1; citation_publication_date=2006; citation_pages=315-325; citation_doi=10.1016/j.jmaa.2006.01.063; citation_id=CR20
Koyuncuoğlu, H.C.:
$$q$$
-Floquet theory and its extensions to time scales periodic in shifts. Ph.D. Thesis, Izmir University of Economics, Izmir, Turkey (2016)
Koyuncuoğlu, H.C.: A generalization of new periodicity concept on time scales. In: Conference Proceedings of 4th International E-Conference on Mathematical Advances and Applications (ICOMAA-2021). Conference Proceedings of Science and Technology (2021)
citation_journal_title=Filomat; citation_title=Unified Massera type theorems for dynamic equations on time scales; citation_author=HC Koyuncuoğlu; citation_volume=37; citation_issue=8; citation_publication_date=2023; citation_pages=2405-2419; citation_doi=10.2298/FIL2308405K; citation_id=CR23
citation_journal_title=Sci. China Ser. A.; citation_title=Existence and global attractivity of positive periodic solution for a class of delay differential equations; citation_author=Y Li; citation_volume=41; citation_publication_date=1998; citation_pages=273-284; citation_doi=10.1007/BF02879046; citation_id=CR24
citation_journal_title=J. Nonlinear Math. Phys.; citation_title=Darboux transformations for
-discretizations of
second order differential equations; citation_author=P Malkiewicz, M Nieszporski; citation_volume=12; citation_issue=2; citation_publication_date=2013; citation_pages=231-239; citation_doi=10.2991/jnmp.2005.12.s2.17; citation_id=CR25
citation_journal_title=Arch. Math.; citation_title=The approximation by
-Bernstein polynomials in the case
; citation_author=S Ostorovska; citation_volume=86; citation_publication_date=2006; citation_pages=282-288; citation_doi=10.1007/s00013-005-1503-y; citation_id=CR26
citation_journal_title=Compos. Math.; citation_title=
-Adic confluence of
-difference equations; citation_author=A Pulita; citation_volume=144; citation_issue=4; citation_publication_date=2008; citation_pages=867-919; citation_doi=10.1112/S0010437X07003454; citation_id=CR27
citation_journal_title=Math. Comput. Model.; citation_title=Periodic solution of single population models on time scales; citation_author=J Zhang, M Fan, H Zhu; citation_volume=52; citation_issue=3–4; citation_publication_date=2010; citation_pages=515-521; citation_doi=10.1016/j.mcm.2010.03.048; citation_id=CR28