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

Let $M_γ$ be precise a priori majorant of first eigenvalues of Sturm--Liouville problems $-y"+qy=λy,\quad y(0)=y(1)=0$, where $q\leqslant 0$ and $\int_0^1 |q|^γ\,dx=1$, $γ\in (0,1/2)$. It is shown that the inequality $M_γ<π^2$ is true.

No reviews yet.

No comments yet.