On the number of real zeroes of a homogeneous differential polynomial and a generalization of the Hawaii conjecture

Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova

For a given real polynomial $p$ we study the possible number of real roots of a differential polynomial $H_{\varkappa}[p](x) = \varkappa\left(p'(x)\right)^2-p(x)p''(x), \varkappa \…