# The Riccati differential equation with complex-valued coefficients and application to the equation ${x}^{\text{'}\text{'}}+P\left(t\right){x}^{\text{'}}+Q\left(t\right)x=0$

Archivum Mathematicum (1982)

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

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topDošlá, 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

top- Butlewski A., Sur un mouvement plan, Ann. Polon. Math. 13 (1963), 139-161. (1963) Zbl0118.30503MR0153936
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- Ráb M., The Riccati Differential Equation with Complex-valued coefficients, Czechoslovak Math. J. 20 (1970), 491-503. (1970) Zbl0215.14201MR0268452
- 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
- Ráb M., Asymptotic behaviour of the equation $x"+p\left(t\right){x}^{\text{\'}}+q\left(t\right)x=0$ with complex-valued coefficients, Arch. Math. (Brno) 4 (1975), 193-204. (1975) MR0404776
- 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
- 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
- Kalas J., On certain asymptotic properties of the solutions of the equation $\dot{z}=f(t,z)$ with a complex-valued function f, Czech. Math. Journal, to appear. MR0718923
- Kalas J., Asymptotic behaviour of equations $\dot{z}=q(t,z)-p\left(t\right){z}^{2}$ and $\ddot{x}=x\varphi (t,\dot{x}{x}^{-1})$, Arch. Math. (Brno) 17 (1981), 191-206. (1981) MR0672659

## Citations in EuDML Documents

top- Josef Kalas, Some results on the asymptotic behaviour of the equation $\dot{z}=f(t,z)$ with a complex-valued function $f$
- Josef Kalas, Asymptotic behaviour of the equation $\dot{z}=G(t,z)[h\left(z\right)+g(t,z)]$
- Josef Kalas, Contributions to the asymptotic behaviour of the equation $\dot{z}=f(t,z)$ with a complex-valued function $f$
- Josef Kalas, Asymptotic nature of solutions of the equation $\dot{z}=f(t,z)$ with a complex valued function $f$

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