Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order

Werner Kratz

Czechoslovak Mathematical Journal (1988)

  • Volume: 38, Issue: 2, page 351-365
  • ISSN: 0011-4642

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Kratz, Werner. "Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order." Czechoslovak Mathematical Journal 38.2 (1988): 351-365. <http://eudml.org/doc/13710>.

@article{Kratz1988,
author = {Kratz, Werner},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sturm-Liouville problems; Hermitian matrix-solutions; Riccati equation; Hamiltonian system; self-adjoint scalar differential equation},
language = {eng},
number = {2},
pages = {351-365},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order},
url = {http://eudml.org/doc/13710},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Kratz, Werner
TI - Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order
JO - Czechoslovak Mathematical Journal
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 2
SP - 351
EP - 365
LA - eng
KW - Sturm-Liouville problems; Hermitian matrix-solutions; Riccati equation; Hamiltonian system; self-adjoint scalar differential equation
UR - http://eudml.org/doc/13710
ER -

References

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  2. Coddington E. A., Levinson N., Theory of ordinary differential equations, Mc Graw-Hill 1955. (1955) Zbl0064.33002MR0069338
  3. Eastham M. S. P., Grundniewicz С. G. M., 10.1112/jlms/s2-24.2.255, J. London Math. Soc. (2), 24 (1981), 255-271. (1981) MR0631938DOI10.1112/jlms/s2-24.2.255
  4. Eberhard W., Über das asymptotische Verhalten von Lösungen der linearen Differentialgleichung M [ y ] = λ N [ y ] für große Werte von λ , Math. Z. 119 (1971), 160-170. (1971) Zbl0198.12001MR0284658
  5. Kratz W., А substitute of l'Hospital's rule for matrices, To appear in the Proc. Amer. Math. Soc. Zbl0629.15014MR0875370
  6. Kratz W., Peyerimhoff A., 10.1524/anly.1985.5.12.97, Analysis 5 (1985), 97-152. (1985) Zbl0541.34013MR0791495DOI10.1524/anly.1985.5.12.97
  7. Neumark M. A., Lineare Differentialoperatoren, Akademie-Verlag 1967. (1967) MR0216049
  8. Reid W. T., Ordinary differential equations, Wiley 1971. (1971) Zbl0212.10901MR0273082
  9. Reid W. T., Riccati differential equations, Academic Press 1972. (1972) Zbl0254.34003MR0357936
  10. Swanson C. A., Picone's identity, Rend. Mat. (6) 8 (1975), 373-397. (1975) Zbl0327.34028MR0402188
  11. Wilkinson J. H., The algebraic eigenvalue problem, Clarendon Press 1965. (1965) Zbl0258.65037MR0184422
  12. Wolter M., 10.1007/BF01218374, Math. Z. 178 (1981), 99-113. (1981) Zbl0448.34021MR0627097DOI10.1007/BF01218374

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