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  • Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator <p> <center> l(y)=1/w(t) \sum<sub>k=0</sub><sup>n</sup> [ p<sub>k</sub>(t) y<sup>(k)</sup> ]<sup>(k)</sup> on [a,\infty), </center> </p> <p> is established. This condition is based on a recently proved generalized reciprocity principle for l and on the relationship between spectral properties of l and oscillation of a certain associated (2n-2)-order differential equation. An application to ''Euler-type'' fourth order operator is given.</p>
  • Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator <p> <center> l(y)=1/w(t) \sum<sub>k=0</sub><sup>n</sup> [ p<sub>k</sub>(t) y<sup>(k)</sup> ]<sup>(k)</sup> on [a,\infty), </center> </p> <p> is established. This condition is based on a recently proved generalized reciprocity principle for l and on the relationship between spectral properties of l and oscillation of a certain associated (2n-2)-order differential equation. An application to ''Euler-type'' fourth order operator is given.</p> (en)
  • Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator <p> <center> l(y)=1/w(t) \sum<sub>k=0</sub><sup>n</sup> [ p<sub>k</sub>(t) y<sup>(k)</sup> ]<sup>(k)</sup> on [a,\infty), </center> </p> <p> is established. This condition is based on a recently proved generalized reciprocity principle for l and on the relationship between spectral properties of l and oscillation of a certain associated (2n-2)-order differential equation. An application to ''Euler-type'' fourth order operator is given.</p> (cs)
Title
  • Spectral properties of general self-adjoint, even order differential operators
  • Spectral properties of general self-adjoint, even order differential operators (en)
  • Spectral properties of general self-adjoint, even order differential operators (cs)
skos:prefLabel
  • Spectral properties of general self-adjoint, even order differential operators
  • Spectral properties of general self-adjoint, even order differential operators (en)
  • Spectral properties of general self-adjoint, even order differential operators (cs)
skos:notation
  • RIV/00216224:14310/00:00008154!RIV08-GA0-14310___
http://linked.open.../vavai/riv/strany
  • 165-186
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/96/0410)
http://linked.open...iv/cisloPeriodika
  • 2
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  • 727310
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  • RIV/00216224:14310/00:00008154
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  • (non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • SK - Slovenská republika
http://linked.open...ontrolniKodProRIV
  • [B5C9D94F9240]
http://linked.open...i/riv/nazevZdroje
  • Mathematica Slovaca
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http://linked.open...ichTvurcuVysledku
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http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 50
http://linked.open...iv/tvurceVysledku
  • Hilscher, Roman
issn
  • 0139-9918
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http://localhost/t...ganizacniJednotka
  • 14310
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