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Averaging techniques and oscillation of quasilinear elliptic equations

Zhi-Ting Xu, Bao-Guo Jia, Shao-Yuan Xu (2004)

Annales Polonici Mathematici

By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order i , j = 1 N D i [ A i j ( x ) | D y | p - 2 D j y ] + p ( x ) f ( y ) = 0 are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.

Basic algebro-geometric conceps in the study of planar polynomial vector fields.

Dana Schlomiuk (1997)

Publicacions Matemàtiques

In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.

Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation

Zdeněk Kadeřábek (2016)

Archivum Mathematicum

The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....

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