Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
The Beverton–Holt q-Difference Equation with Periodic Growth Rate Read chapter Read first chapter

2015 | OriginalPaper | Chapter

6. Generalized Zeros and Nonpositivity of Energy Functionals Associated with Half-Linear Even-Order Difference Equations

Author : Ondřej Došlý

Published in: Difference Equations, Discrete Dynamical Systems and Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We investigate the relationship between oscillatory properties of half-linear even order difference equations and nonpositivity of the associated energy functionals. We convert the investigated difference equation into a Hamiltonian type difference system and using this transformation we establish our main result which says that the existence of two (or more) generalized zeros of a solution of the investigated difference equation implies that the corresponding energy functional attains a nonpositive value.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter On Hausdorff Dimension of Invariant Sets for a Class of Piecewise Linear Maps
next chapter Eigenvalue Comparison for Discrete Symplectic Systems
Literature
1.
R.P. Agarwal, M. Bohner, S.R. Grace, D. O’Regan, Discrete Oscillation Theory (Hindawi Publishing Corporation, Cairo, 2006)MATH
2.
C.D. Ahlbrandt, A.C. Peterson, The \((n, n)\) disconjugacy of a 2nth-order linear difference equation. Comput. Appl. Math. 28, 1–9 (1994)MathSciNetCrossRefMATH
3.
I. Bihari, An oscillation theorem concerning the half-linear differential equation of second order, Magyar Tud. Akad. Mat. Kutató Int. Közl. 8, 275–280 (1964)MathSciNetMATH
4.
M. Bohner, Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. J. Math. Anal. Appl. 199, 804–826 (1996)MathSciNetCrossRefMATH
5.
M. Bohner, On disconjugacy for Sturm-Liouville difference equations, in Difference Equations: Theory and Applications, (San Francisco, CA, 1995). (J. Differ. Equations Appl. 2 (1996), no. 2, 227–237)
6.
O. Došlý, Oscillation criteria for higher order Sturm-Liouville difference equations. J. Differ. Equ. Appl. 4(5), 425–450 (1998)MathSciNetCrossRefMATH
7.
O. Došlý, Oscillation and spectral properties of self-adjoint even order differential operators with middle terms, Proceedings of the 7th Colloquium on the Qualitative Theory of Differential Equations (2004) No. 7, p. 21. (Proc. Colloq. Qual. Theory Differ. Equ. 7, Electron J. Qual Theory Differ. Equ. Szeged
8.
O. Došlý, R. Hilscher, A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD, advances in difference equations, IV. Comput. Math. Appl. 45 no. 6–9, 961–981 (2003)
9.
O. Došlý, P. Řehák, Nonoscillation criteria for half-linear second-order difference equations, advances in difference equations, III. Comput. Math. Appl. 42(3–5), 453–464 (2001)MathSciNetMATH
10.
O. Došlý, P. Řehák, Half-Linear Differential Equations. North Holland Mathematics Studies, vol. 202 (Elsevier, Amsterdam, 2005)
11.
O. Došlý, V. Růžička, Nonoscillation of Higher Order Half-Linear Differential Equations. Electron. J. Qual. Theory Differ. Equ. 19, 15 (2015)
12.
W.D. Evans, M.K. Kwong, A. Zettl, Lower bounds for spectrum of ordinary differential operators. J. Differ. Equ. 48, 123–155 (1983)MathSciNetCrossRefMATH
13.
S. Fišnarová, Oscillation of two-term Sturm-Liouville difference equations. Int. J. Differ. Equ. 1(1), 81–99 (2006)MathSciNetMATH
14.
I.M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Program for Scientific Translations, Jerusalem, 1965 (Daniel Davey & Co. Inc., New York, 1966)
15.
16.
P. Hartman, Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity. Trans. Am. Math. Soc. 246, 1–30 (1978)MathSciNetMATH
17.
R. Oinarov, S.Y. Rakhmatulina, Oscillation and nonoscillatorion of two terms linear and half-linear equations of higher order, Electron. J. Qual. Theory Differ. Equ. 2010 No. 49, 1–15 (2010)
18.
S. Peña, Discrete spectra criteria for singular difference operators. Math. Bohem. 124(1), 35–44 (1999)MathSciNetMATH
19.
20.
P. Řehák, Oscillatory properties of second order half-linear difference equations. Czechoslov. Math. J. 51(126), 303–321 (2001)MathSciNetMATH
21.
P. Řehák, Generalized discrete Riccati equation and oscillation of half-linear difference equations. Math. Comput. Model. 34, 257–269 (2001)MathSciNetCrossRefMATH
22.
P. Řehák, Comparison theorems and strong oscillation in the half-linear discrete oscillation theory, Rocky Mountain J. Math. 33, 333–352 (2003)
23.
J. Weidmann, Spectral theory of ordinary differential operators, Lecture Notes in Mathematics, vol. 1258 (Springer-Verlag, Berlin, 1987)
Metadata
Title
Generalized Zeros and Nonpositivity of Energy Functionals Associated with Half-Linear Even-Order Difference Equations
Author
Ondřej Došlý
Copyright Year
2015
Book
Difference Equations, Discrete Dynamical Systems and Applications

Print ISBN: 978-3-319-24745-8

Electronic ISBN: 978-3-319-24747-2

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-24747-2_6

Premium Partner

    Image Credits