Characteristic numbers of non‐autonomous emden‐fowler type equations

Abstract

We consider the Emden‐Fowler equation x” = ‐q(t)|x|^2εx, ^ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number A_n 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|^2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b).

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.

Key words:

• Characteristic numbers
• Emden‐Fowler equation
• Nehari's solutions