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
Asymptotic conditions at the two first eigenvalues for the periodic solutions of Liénard differential equations and an inequality of E. Schmidt cover
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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’’(t) + f(x(t)) x’(t) + g(t, x(t)) = e(t),
x(0)x(2π)=x(0)x(2π)=0x(0) — x(2 \pi) = x’(0) —x’(2 \pi) = 0

under some non-resonance conditions on the asymptotic behavior of x1g(t,x)x^{-1}g(t, x) for x|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