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On the limit cycle of the Liénard equation

Kenzi Odani — 2000

Archivum Mathematicum

In the paper, we give an existence theorem of periodic solution for Liénard equation x ˙ = y - F ( x ) , y ˙ = - g ( x ) . As a result, we estimate the amplitude ρ ( μ ) (maximal x -value) of the limit cycle of the van der Pol equation x ˙ = y - μ ( x 3 / 3 - x ) , y ˙ = - x from above by ρ ( μ ) < 2 . 3439 for every μ 0 . The result is an improvement of the author’s previous estimation ρ ( μ ) < 2 . 5425 .

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