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Characteristic numbers of non‐autonomous emden‐fowler type equations

    A. Gritsans Affiliation
    ; F. Sadyrbaev Affiliation

Abstract

We consider the Emden‐Fowler equation x” = ‐q(t)|x|x, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|x, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (ab).


The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution.  


First Published Online: 14 Oct 2010

Keyword : characteristic numbers, Emden‐Fowler equation, Nehari's solutions

How to Cite
Gritsans, A., & Sadyrbaev, F. (2006). Characteristic numbers of non‐autonomous emden‐fowler type equations. Mathematical Modelling and Analysis, 11(3), 243-252. https://doi.org/10.3846/13926292.2006.9637316
Published in Issue
Sep 30, 2006
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