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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 .

On the limits of solutions of functional differential equations

Mihály Pituk (1993)

Mathematica Bohemica

Our aim in this paper is to obtain sufficient conditions under which for every ξ R n there exists a solution x of the functional differential equation x ˙ ( t ) = c t [ d s Q ( t , s ) ] f ( t , x ( s ) ) , t [ t 0 , T ] such that l i m t T - x ( t ) = ξ .

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