The Riccati differential equation with complex-valued coefficients and application to the equation x ' ' + P ( t ) x ' + Q ( t ) x = 0

Zuzana Došlá

Archivum Mathematicum (1982)

  • Volume: 018, Issue: 3, page 133-143
  • ISSN: 0044-8753

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Došlá, Zuzana. "The Riccati differential equation with complex-valued coefficients and application to the equation $x^{\prime \prime }+P(t)x^{\prime }+Q(t)x=0$." Archivum Mathematicum 018.3 (1982): 133-143. <http://eudml.org/doc/18087>.

@article{Došlá1982,
author = {Došlá, Zuzana},
journal = {Archivum Mathematicum},
keywords = {Riccati equation; Lyapunov function},
language = {eng},
number = {3},
pages = {133-143},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The Riccati differential equation with complex-valued coefficients and application to the equation $x^\{\prime \prime \}+P(t)x^\{\prime \}+Q(t)x=0$},
url = {http://eudml.org/doc/18087},
volume = {018},
year = {1982},
}

TY - JOUR
AU - Došlá, Zuzana
TI - The Riccati differential equation with complex-valued coefficients and application to the equation $x^{\prime \prime }+P(t)x^{\prime }+Q(t)x=0$
JO - Archivum Mathematicum
PY - 1982
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 018
IS - 3
SP - 133
EP - 143
LA - eng
KW - Riccati equation; Lyapunov function
UR - http://eudml.org/doc/18087
ER -

References

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  1. Butlewski A., Sur un mouvement plan, Ann. Polon. Math. 13 (1963), 139-161. (1963) Zbl0118.30503MR0153936
  2. Kulig C., On a System of Differential Equations, Zeszyty Naukowe Univ. Jagiellonskiego, Prace Mat., Zeszyt 9, LXXVII (1963), 37-48. (1963) Zbl0267.34029MR0204763
  3. Ráb M., The Riccati Differential Equation with Complex-valued coefficients, Czechoslovak Math. J. 20 (1970), 491-503. (1970) Zbl0215.14201MR0268452
  4. Ráb M., Geometrical approach to the study of the Riccati differential equation with complex-valued coefficients, Journal of Differential Equations 25 (1977), 108-114. (1977) MR0492454
  5. Ráb M., Asymptotic behaviour of the equation x " + p ( t ) x ' + q ( t ) x = 0 with complex-valued coefficients, Arch. Math. (Brno) 4 (1975), 193-204. (1975) MR0404776
  6. Kalas J., Asymptotic behaviour of the solutions of the equation dz/dt = f(t, z) with a complex-valued function f, Colloquia Mathematica Societatis János Bolyai, 30. Qualitative Theory of Differential Equations, Szeged (Hungary) 1979, pp. 431-462. (1979) MR0680606
  7. Kalas J., On the asymptotic behaviour of the equation dz/dt =f(t,z) with a complex-valued function f, Arch. Math. (Brno) 17 (1981), 11-12. (1981) Zbl0475.34028MR0672484
  8. Kalas J., On certain asymptotic properties of the solutions of the equation z ˙ = f ( t , z ) with a complex-valued function f, Czech. Math. Journal, to appear. MR0718923
  9. Kalas J., Asymptotic behaviour of equations z ˙ = q ( t , z ) - p ( t ) z 2 and x ¨ = x ϕ ( t , x ˙ x - 1 ) , Arch. Math. (Brno) 17 (1981), 191-206. (1981) MR0672659

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