Massera’s theorem in quantum calculus
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- by Martin Bohner and Jaqueline G. Mesquita PDF
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Abstract:
In this paper, we present versions of Massera’s theorem for linear and nonlinear $q$-difference equations and present some examples to illustrate our results.References
- Martin Bohner and Rotchana Chieochan, Floquet theory for $q$-difference equations, Sarajevo J. Math. 8(21) (2012), no. 2, 355–366. MR 3057892, DOI 10.5644/SJM.08.2.14
- Martin Bohner and Rotchana Chieochan, The Beverton–Holt $q$-difference equation, J. Biol. Dyn. 7 (2013), no. 1, 86–95.
- Martin Bohner and Rotchana Chieochan, Positive periodic solutions for higher-order functional $q$-difference equations, J. Appl. Funct. Anal. 8 (2013), no. 1, 14–22. MR 3060159
- Martin Bohner and Jaqueline G. Mesquita, Periodic averaging principle in quantum calculus, J. Math. Anal. Appl. 435 (2016), no. 2, 1146–1159. MR 3429633, DOI 10.1016/j.jmaa.2015.10.078
- Martin Bohner and Allan Peterson, Dynamic equations on time scales, Birkhäuser Boston, Inc., Boston, MA, 2001. An introduction with applications. MR 1843232, DOI 10.1007/978-1-4612-0201-1
- Martin Bohner and Sabrina H. Streipert, The Beverton-Holt $q$-difference equation with periodic growth rate, Difference equations, discrete dynamical systems and applications, Springer Proc. Math. Stat., vol. 150, Springer, Cham, 2015, pp. 3–14. MR 3477511, DOI 10.1007/978-3-319-24747-2_{1}
- Martin Bohner and Sabrina Streipert, Optimal harvesting policy for the Beverton-Holt quantum difference model, Math. Morav. 20 (2016), no. 2, 39–57. MR 3554523, DOI 10.5937/matmor1602039b
- Martin Bohner and Sabrina H. Streipert, The second Cushing-Henson conjecture for the Beverton-Holt $q$-difference equation, Opuscula Math. 37 (2017), no. 6, 795–819. MR 3708973, DOI 10.7494/OpMath.2017.37.6.795
- T. A. Burton, Stability and periodic solutions of ordinary and functional differential equations, Dover Publications, Inc., Mineola, NY, 2005. Corrected version of the 1985 original. MR 2761514
- Khalil Ezzinbi, Samir Fatajou, and Gaston Mandata N’guérékata, Massera-type theorem for the existence of $C^{(n)}$-almost-periodic solutions for partial functional differential equations with infinite delay, Nonlinear Anal. 69 (2008), no. 4, 1413–1424. MR 2426702, DOI 10.1016/j.na.2007.06.041
- Khalil Ezzinbi and Gaston M. N’Guérékata, Massera type theorem for almost automorphic solutions of functional differential equations of neutral type, J. Math. Anal. Appl. 316 (2006), no. 2, 707–721. MR 2207341, DOI 10.1016/j.jmaa.2005.04.074
- George Gasper and Mizan Rahman, Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 96, Cambridge University Press, Cambridge, 2004. With a foreword by Richard Askey. MR 2128719, DOI 10.1017/CBO9780511526251
- Victor Kac and Pokman Cheung, Quantum calculus, Universitext, Springer-Verlag, New York, 2002. MR 1865777, DOI 10.1007/978-1-4613-0071-7
- A. Lavagno, A. M. Scarfone, and P. Narayana Swamy, Basic-deformed thermostatistics, J. Phys. A 40 (2007), no. 30, 8635–8654. MR 2344514, DOI 10.1088/1751-8113/40/30/003
- A. Lavagno and P. Narayana Swamy, $q$-deformed structures and nonextensive statistics: a comparative study, Phys. A 305 (2002), no. 1-2, 310–315. Non extensive thermodynamics and physical applications (Villasimius, 2001). MR 1923946, DOI 10.1016/S0378-4371(01)00680-X
- Xi-Lan Liu and Wan-Tong Li, Periodic solutions for dynamic equations on time scales, Nonlinear Anal. 67 (2007), no. 5, 1457–1463. MR 2323293, DOI 10.1016/j.na.2006.07.030
- James Liu, Gaston N’Guérékata, and Nguyen van Minh, A Massera type theorem for almost automorphic solutions of differential equations, J. Math. Anal. Appl. 299 (2004), no. 2, 587–599. MR 2098262, DOI 10.1016/j.jmaa.2004.05.046
- Satoru Murakami, Toshiki Naito, and Nguyen Van Minh, Massera’s theorem for almost periodic solutions of functional differential equations, J. Math. Soc. Japan 56 (2004), no. 1, 247–268. MR 2027625, DOI 10.2969/jmsj/1191418705
- Toshiki Naito, Nguyen Van Minh, and Jong Son Shin, A Massera type theorem for functional differential equations with infinite delay, Japan. J. Math. (N.S.) 28 (2002), no. 1, 31–49. MR 1933476, DOI 10.4099/math1924.28.31
- Andrew Strominger, Black hole statistics, Phys. Rev. Lett. 71 (1993), no. 21, 3397–3400. MR 1246067, DOI 10.1103/PhysRevLett.71.3397
- Li Yong, Lin Zhenghua, and Li Zhaoxing, A Massera type criterion for linear functional-differential equations with advance and delay, J. Math. Anal. Appl. 200 (1996), no. 3, 717–725. MR 1393112, DOI 10.1006/jmaa.1996.0235
Additional Information
- Martin Bohner
- Affiliation: Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte 70910-900, Brasília-DF, Brazil
- MR Author ID: 295863
- ORCID: 0000-0001-8310-0266
- Email: bohner@mst.edu
- Jaqueline G. Mesquita
- Affiliation: Departamento de Matemática, Universidade de Brasília, Campus Universitário Darcy Ribeiro, Asa Norte 70910-900, Brasília-DF, Brazil
- MR Author ID: 940198
- Email: jgmesquita@unb.br
- Received by editor(s): October 24, 2017
- Received by editor(s) in revised form: February 4, 2018
- Published electronically: August 8, 2018
- Communicated by: Mourad E. H. Ismail
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4755-4766
- MSC (2010): Primary 39A20, 34N05, 34C25, 39A23
- DOI: https://doi.org/10.1090/proc/14116
- MathSciNet review: 3856143