%0 Journal Article
%A Giraldo Suárez, Luis
%A Gascón, Francisco G.
%T New proof and generalizations of the Demidowitsch-Schneider criterion
%D 2000
%@ 1089-7658
%U https://hdl.handle.net/20.500.14352/57586
%X Analysis of the question whether or not a given dynamical system has closed trajectories is of great importance for applications and represents independent theoretical interest. The authors give a new geometrical proof of the extension of the Bendixson-Dulac criterion on the absence of closed trajectories in R3 obtained by V. B. Demidovich [Z. Angew. Math. Mech. 46, 145-146 (1966; Zbl 0138.33303)] and corrected later by K. R. Schneider [Z. Angew. Math. Mech. 49, 441-443 (1969; Zbl 0186.15603)]. Due to the flexibility of the new approach, extensions of the Demidovich criterion to several directions have been obtained. Illustrative examples are considered and someopen problems are discussed.
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