Spectral properties of fourth order differential operators

Ondřej Došlý; Roman Hilscher

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 2, page 153-168
  • ISSN: 0862-7959

Abstract

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ℓ ( y ) ≡ 1 w ( t ) ( r ( t ) y ) , t ∈ [ a , ∞ ) are established. These conditions are based on a recently proved relationship between spectral properties of ℓ and oscillation of a certain associated second order differential equation.

How to cite

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Došlý, Ondřej, and Hilscher, Roman. "Spectral properties of fourth order differential operators." Mathematica Bohemica 122.2 (1997): 153-168. <http://eudml.org/doc/248150>.

@article{Došlý1997,
abstract = {Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $\ell (y)\equiv \{1\over w(t)\}\{(r(t)\{y\})\}$, $t\in [a,\infty )$ are established. These conditions are based on a recently proved relationship between spectral properties of $\ell $ and oscillation of a certain associated second order differential equation.},
author = {Došlý, Ondřej, Hilscher, Roman},
journal = {Mathematica Bohemica},
keywords = {singular differential operators; property BD; oscillation criteria; principal solution; singular differential operators; property BD; oscillation criteria; principal solution},
language = {eng},
number = {2},
pages = {153-168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral properties of fourth order differential operators},
url = {http://eudml.org/doc/248150},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Došlý, Ondřej
AU - Hilscher, Roman
TI - Spectral properties of fourth order differential operators
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 2
SP - 153
EP - 168
AB - Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $\ell (y)\equiv {1\over w(t)}{(r(t){y})}$, $t\in [a,\infty )$ are established. These conditions are based on a recently proved relationship between spectral properties of $\ell $ and oscillation of a certain associated second order differential equation.
LA - eng
KW - singular differential operators; property BD; oscillation criteria; principal solution; singular differential operators; property BD; oscillation criteria; principal solution
UR - http://eudml.org/doc/248150
ER -

References

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  10. D. B. Hinton R. T. Lewis, Discrete spectra criteria for singular differential operators with middle terms, Math. Proc. Cambridge Philos. Soc. 77 (1975), 337-347. (1975) MR0367358
  11. R. T. Lewis, 10.1090/S0002-9939-1974-0330608-8, Proc. Amer. Mat. Soc. 42 (1974), 480-482. (1974) MR0330608DOI10.1090/S0002-9939-1974-0330608-8
  12. M. A. Naimark, Linear Differential Operators, Part II. Ungar, New York, 1968. (1968) Zbl0227.34020
  13. W. T. Reid, Sturmian Theory for Ordinary Differential Equations, Springer-Verlag, New York, 1980. (1980) Zbl0459.34001MR0606199
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  16. J. Weidmann, Linear Operators in Hilbert Spaces, Springer-Verlag, New York, 1980. (1980) Zbl0434.47001MR0566954

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