The Sturm--Liouville problem with singular potential and the extrema of the first eigenvalue

Abstract

On the basis of the theory of Sturm--Liouville problem with distribution coefficients we get the infima and suprema of the first eigenvalue of the problem $-y"+(q-\lambda )y=0,y^{\prime }(0)-k_0^{2}y(0)=y^{\prime }(1)+k_1^{2}y(1)=0$, where $q$ belongs to the set of constant-sign summable functions on $[0,1]$ such that ${\int }_0^{1}qdx=\pm 1$.

12 pages