Skip to main content
Erschienen in:
Buchtitelbild

2020 | OriginalPaper | Buchkapitel

Linearized Oscillation Theory for a Nonlinear Nonautonomous Difference Equation

verfasst von : Elena Braverman, Başak Karpuz

Erschienen in: Difference Equations and Discrete Dynamical Systems with Applications

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We review some theorems and mistakes in linearized oscillation results for difference equations with variable coefficients and constant delays, as well as develop linearized oscillation theory when delays are also variable. Main statements are applied to discrete models of population dynamics. In particular, oscillation of generalized Pielou, Ricker and Lasota–Wazewska equations is considered.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Allen, L.J.S.: An Introduction to Mathematical Biology. Pearson Prentice Hall, Upper Saddle River (2006) Allen, L.J.S.: An Introduction to Mathematical Biology. Pearson Prentice Hall, Upper Saddle River (2006)
2.
Zurück zum Zitat Baštinec, J., Berezansky, L., Diblík, J., Šmarda, Z.: On the critical case in oscillation for differential equations with a single delay and with several delays. Abstr. Appl. Anal. Article ID 417869 (2010) Baštinec, J., Berezansky, L., Diblík, J., Šmarda, Z.: On the critical case in oscillation for differential equations with a single delay and with several delays. Abstr. Appl. Anal. Article ID 417869 (2010)
3.
Zurück zum Zitat Berezansky, L., Braverman, E.: On existence of positive solutions for linear difference equations with several delays. Adv. Dyn. Syst. Appl. 1, 29–47 (2006)MathSciNetMATH Berezansky, L., Braverman, E.: On existence of positive solutions for linear difference equations with several delays. Adv. Dyn. Syst. Appl. 1, 29–47 (2006)MathSciNetMATH
4.
Zurück zum Zitat Braverman, E., Karpuz, B.: On monotonicity of nonoscillation properties of dynamic equations in time scales. Z. Anal. Anwend. 31, 203–216 (2012)MathSciNetCrossRef Braverman, E., Karpuz, B.: On monotonicity of nonoscillation properties of dynamic equations in time scales. Z. Anal. Anwend. 31, 203–216 (2012)MathSciNetCrossRef
5.
Zurück zum Zitat Chen, M.P., Yu, J.S.: Oscillation and global attractivity in the discrete Lasota–Wazewska model. Soochow J. Math. 25, 1–9 (1999)MathSciNetMATH Chen, M.P., Yu, J.S.: Oscillation and global attractivity in the discrete Lasota–Wazewska model. Soochow J. Math. 25, 1–9 (1999)MathSciNetMATH
6.
Zurück zum Zitat Elaydi, S.: An Introduction to Difference Equations. Undergraduate Texts in Mathematics, 3rd edn. Springer, New York (2005)MATH Elaydi, S.: An Introduction to Difference Equations. Undergraduate Texts in Mathematics, 3rd edn. Springer, New York (2005)MATH
7.
Zurück zum Zitat Győri, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Oxford University Press, New York (1991)MATH Győri, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Oxford University Press, New York (1991)MATH
8.
Zurück zum Zitat Pielou, E.C.: An Introduction to Mathematical Ecology. Wiley, New York (1969)MATH Pielou, E.C.: An Introduction to Mathematical Ecology. Wiley, New York (1969)MATH
9.
Zurück zum Zitat Tang, S., Xiao, Y., Chen, J.F.: Linearized oscillations in nonlinear delay difference equations. Acta Math. Sin. (Engl. Ser.) 15, 569–574 (1999)MathSciNetCrossRef Tang, S., Xiao, Y., Chen, J.F.: Linearized oscillations in nonlinear delay difference equations. Acta Math. Sin. (Engl. Ser.) 15, 569–574 (1999)MathSciNetCrossRef
10.
Zurück zum Zitat Tang, X.H., Yu, J.S.: Oscillation of nonlinear delay difference equations. J. Math. Anal. Appl. 249, 476–490 (2000)MathSciNetCrossRef Tang, X.H., Yu, J.S.: Oscillation of nonlinear delay difference equations. J. Math. Anal. Appl. 249, 476–490 (2000)MathSciNetCrossRef
11.
Zurück zum Zitat Tang, X.H., Yu, J.S.: Oscillations of delay difference equations in a critical state. Appl. Math. Lett. 13, 9–15 (2000)MathSciNetCrossRef Tang, X.H., Yu, J.S.: Oscillations of delay difference equations in a critical state. Appl. Math. Lett. 13, 9–15 (2000)MathSciNetCrossRef
12.
Zurück zum Zitat Wang, Z.C., Zhang, R.Y.: Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients. Comput. Math. Appl. 40, 705–712 (2000)MathSciNetCrossRef Wang, Z.C., Zhang, R.Y.: Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients. Comput. Math. Appl. 40, 705–712 (2000)MathSciNetCrossRef
13.
Zurück zum Zitat Ważewska-Czyżewska, M., Lasota, A.: Mathematical problems of the dynamics of a system of red blood cells. Mat. Stos. 3(6), 23–40 (1976)MathSciNet Ważewska-Czyżewska, M., Lasota, A.: Mathematical problems of the dynamics of a system of red blood cells. Mat. Stos. 3(6), 23–40 (1976)MathSciNet
14.
Zurück zum Zitat Yan, J.R., Qian, C.X.: Oscillation and comparison results for delay difference equations. J. Math. Anal. Appl. 165, 346–360 (1992)MathSciNetCrossRef Yan, J.R., Qian, C.X.: Oscillation and comparison results for delay difference equations. J. Math. Anal. Appl. 165, 346–360 (1992)MathSciNetCrossRef
15.
Zurück zum Zitat Zhou, Y.: Oscillation and nonoscillation for difference equations with variable delays. Appl. Math. Lett. 16, 1083–1088 (2003)MathSciNetCrossRef Zhou, Y.: Oscillation and nonoscillation for difference equations with variable delays. Appl. Math. Lett. 16, 1083–1088 (2003)MathSciNetCrossRef
Metadaten
Titel
Linearized Oscillation Theory for a Nonlinear Nonautonomous Difference Equation
verfasst von
Elena Braverman
Başak Karpuz
Copyright-Jahr
2020
DOI
https://doi.org/10.1007/978-3-030-35502-9_1