The extrema of the first eigenvalue of the Sturm--Liouville problem with third-type boundary conditions

Abstract

We get the infima and suprema of the first eigenvalue of the problem $y^{\prime \prime }+qy+\lambda y=0$, $y^{\prime }(0)-k_0^{2}y(0)=y^{\prime }(1)+k_1^{2}y(1)=0$, where $q$ belongs to the set of nonnegative summable functions on [0,1] such that ${\int }_0^1{q}^{\gamma }dx=1$, where $\gamma \in R\setminus \{0\}$.

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