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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 1, 1984, pp. 33–42
DOI: 10.4171/ZAA/88a

Published online: 1984-02-29

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

C.P. Gupta[1] and Jean Mawhin[2]

(1) Northern Illinois University, Dekalb, USA
(2) Université Catholique de Louvain, Belgium

We study the periodic boundary problem $$x’’(t) + f(x(t)) x’(t) + g(t, x(t)) = e(t),$$ $$x(0) — x(2 \pi) = x’(0) —x’(2 \pi) = 0$$ under some non-resonance conditions on the asymptotic behavior of $x^{-1}g(t, x)$ for $|x| \to \infty$.

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Gupta C.P., Mawhin Jean: 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), 33-42. doi: 10.4171/ZAA/88a