On a lower a priori estimate of minimal eigenvalue of one Sturm-Liouville problem with second-type boundary conditions

A. A. Vladimirov, E. S. Karulina

It is proved that for class $A_{\gamma }=\{q\in L_1[0,1]:q\ge 0,{\int }_0^1{q}^{\gamma }dx=1\}$, where $\gamma \in (0,1)$, there exists a potential $q_{\ast }\in A_{\gamma }$ such that minimal eigenvalue ${\lambda }_1(q_{\ast })$…