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On the maximum number of limit cycles of certain polynomial Lienard equations

Posted on:1996-07-02Degree:Ph.DType:Dissertation
University:University of Illinois at Urbana-ChampaignCandidate:Yao, LeummimFull Text:PDF
GTID:1460390014485277Subject:Mathematics
Abstract/Summary:
We consider the Lienard equation of the form;We establish a sharp upper bound for the number of limit cycles (nontrivial isolated periodic orbits of system (2) depending on m and the degree of f provided ;This result is an important step in the study of planar polynomial vector fields in connection with the second part of Hilbert's Sixteenth Problem, which is still an open question.
Keywords/Search Tags:Limit cycles
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