On some a priori majorant of eigenvalues of Sturm--Liouville problems

Abstract

Let $M_{\gamma }$ be precise a priori majorant of first eigenvalues of Sturm--Liouville problems $-y"+qy=\lambda y,y(0)=y(1)=0$, where $q⩽0$ and ${\int }_0^1|q{|}^{\gamma }dx=1$, $\gamma \in (0,1/2)$. It is shown that the inequality $M_{\gamma }<{\pi }^2$ is true.

2 pages