The asymptotic behaviour of q-difference equations with multiple delays

[1] BOHNER, M.-PETERSON, A.: Dynamic Equations on Time Scales. An Introductionwith Applications. Birkh˝auser, Basel, 2001.10.1007/978-1-4612-0201-1Search in Google Scholar

[2] BOHNER, M.-PETERSON, A.: Advances in Dynamic Equations on Time Scales. Birkh˝auser, Boston, MA, 2003.10.1007/978-0-8176-8230-9Search in Google Scholar

[3] BOHNER, M.-¨UNAL, M.: Kneser’s theorem in q-calculus, J. Phys. A 38 (2005), 6729-6739.10.1088/0305-4470/38/30/008Search in Google Scholar

[4] ČERMÁK, J.: The asymptotic bounds of solutions of linear delay systems, J. Math. Anal. Appl. 225 (1998), 373-388.10.1006/jmaa.1998.6018Search in Google Scholar

[5] ČERMÁK, J.: On the asymptotics of solutions of delay dynamic equations on time scales, Math. Comp. Modelling 46 (2007), 455-458.10.1016/j.mcm.2006.11.015Search in Google Scholar

[6] ČERMÁK, J.: On the differential equation with power coefficients and proportional delays, Tatra Mt. Math. Publ. 38 (2007), 57-69.Search in Google Scholar

[7] DERFEL, G.: Functional-differential equations with compressed arguments and polynomialcoefficients: asymptotics of the solutions, J. Math. Anal. Appl. 193 (1995), 671-679.10.1006/jmaa.1995.1260Search in Google Scholar

[8] DERFEL, G.-VOGL, F.: On the asymptotics of solutions of a class of linear functional--differential equations, European J. Appl. Math. 7 (1996), 511-518.10.1017/S0956792500002527Search in Google Scholar

[9] DIBLÍK, J.: Asymptotic behaviour of solutions of linear differential equations with delay, Ann. Polon. Math. LVIII (1993), 131-137.10.4064/ap-58-2-131-137Search in Google Scholar

[10] ELAYDI, S. N.: An Introduction to Difference Equations. Undergrad. Texts Math., Springer-Verlag, New York, NY, 1995.10.1007/978-1-4757-9168-6_3Search in Google Scholar

[11] GYŐRI, I.-PITUK, M.: Comparison theorems and asymptotic equilibrium for delaydifferential and difference equations, Dynam. Systems Appl. 5 (1996) 277-302.Search in Google Scholar

[12] ISERLES, A.: On the generalized pantograph functional-differential equation, European J. Appl. Math. 4 (1993), 1-38.10.1017/S0956792500000966Search in Google Scholar

[13] KATO, T.-MCLEOD, J. B.: The functional differential equation yʹ(x) = ay(λx)+by(x), Bull. Amer. Math. Soc. (N.S.) 77 (1971), 891-937.10.1090/S0002-9904-1971-12805-7Search in Google Scholar

[14] KAC, V.-CHEUNG, P.: Quantum Calculus. Universitext, Springer-Verlag, New York, NY, 2002.10.1007/978-1-4613-0071-7Search in Google Scholar

[15] KUCZMA, M.-CHOCZEWSKI, B.-GER, R.: Iterative Functional Equations. Encyclopedia Math. Appl., Cambridge University Press, Cambridge, 1990.10.1017/CBO9781139086639Search in Google Scholar

[16] LEHNINGER, H.-LIU, Y.: The functional-differential equation yʹ(t) = ay(t)+by(qt)+ cyʹ(qt) + ƒ(t), European J. Appl. Math. 9 (1998), 81-91.10.1017/S0956792597003343Search in Google Scholar

[17] MAKAY, G.-TERJÉKI, J.: On the asymptotic behavior of the pantograph equations, Electron. J. Qual. Theory Differ. Equ. 2 (1998), 1-12 (electronic).10.14232/ejqtde.1998.1.2Search in Google Scholar

[18] OCKENDON, J. R.-TAYLER A. B.: The dynamics of a current collection system foran electric locomotive, Proc. Roy. Soc. London Ser. A. 322 (1971), 447-468.10.1098/rspa.1971.0078Search in Google Scholar

[19] NAGATOMO, K.-KOGA, Y.: q-difference analogue of the Euler-Poisson-Darboux equationand its Laplace sequence, Osaka J. Math. 32 (1995), 451-465.Search in Google Scholar

[20] PANDOLFI, L.: Some observations on the asymptotic behaviors of the solutions of theequation xʹ(t) = a(t)x(λt) + b(t)x(t), λ > 0, J. Math. Anal. Appl. 67 (1979), 483-489.10.1016/0022-247X(79)90038-6Search in Google Scholar