Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt

C.P. Gupta; Jean Mawhin

doi:10.4171/zaa/88a

JournalszaaVol. 3, No. 1pp. 33–42

Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt

C.P. Gupta
Northern Illinois University, Dekalb, USA
Jean Mawhin
Université Catholique de Louvain, Belgium

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Abstract

We study the periodic boundary problem

x ’’ (t) + f (x (t)) x ’ (t) + g (t, x (t)) = e (t),

x (0) — x (2 π) = x ’ (0) — x ’ (2 π) = 0

under some non-resonance conditions on the asymptotic behavior of $x^{- 1} g (t, x)$ for $∣ x ∣ \to \infty$ .

Cite this article

C.P. Gupta, Jean Mawhin, Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt. Z. Anal. Anwend. 3 (1984), no. 1, pp. 33–42

DOI 10.4171/ZAA/88A