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Displaying 181 – 200 of 240

Travaux récents sur les points singuliers des équations différentielles linéaires

Daniel Bertrand (1978/1979)

Séminaire Bourbaki

Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in $ℝ^{n}$ . Also, for symmetric second-order ordinary differential operators we show that ${lim sup}_{t \to c} {(p q^{'})}^{'} / q^{2} = θ < 2$ where $c$ is a singular point guarantees separation of $- {(p y^{'})}^{'} + q y$ on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that $- Δ y + q y$ is separated on its minimal domain if $q$ is superharmonic. For $n = 1$ the criterion...

Ueber Relationen, welche für die zwischen je zwei singulären Punkten erstreckten Integrale der Lösungen linearer Differentialgleichungen stattfinden.

L. Fuchs (1873)

Journal für die reine und angewandte Mathematik

Ueber Relationen zwischen hypergeometrischen Integralen nter Ordnung.

L. Pochhammer (1871)

Journal für die reine und angewandte Mathematik

Unbounded basins of attraction of limit cycles.

Giesl, P. (2003)

Acta Mathematica Universitatis Comenianae. New Series

Uniformly isochronous polynomial centers.

Ivanov, Vladimir V., Volokitin, Evgenii P. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Uniqueness of limit cycles bounded by two invariant parabolas

Eduardo Sáez, Iván Szántó (2012)

Applications of Mathematics

In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.

Uniqueness of limit cycles for a class of cubic systems with two invariant straight lines.

Xie, Xiangdong, Chen, Fengde, Zhan, Qingyi (2010)

Discrete Dynamics in Nature and Society

Versal deformations of $D_{q}$ -invariant 2-parameter families of planar vector fields

Grzegorz Świrszcz (1995)

Annales Polonici Mathematici

The paper deals with 2-parameter families of planar vector fields which are invariant under the group $D_{q}$ for q ≥ 3. The germs at z = 0 of such families are studied and versal families are found. We also give the phase portraits of the versal families.