On positive eigenfunctions of Sturm‐Liouville problem with nonlocal two‐point boundary condition

Abstract

Positive eigenvalues and corresponding eigenfunctions of the linear Sturm‐Liouville problem with one classical boundary condition and another nonlocal two‐point boundary condition are considered in this paper. Four cases of nonlocal two‐point boundary conditions are analysed. We get positive eigenfunctions existence domain for each case of these problems. This domain depends on the parameters of the nonlocal boundary problem and it gives necessary and sufficient conditions for existing positive eigenvalues with positive eigenfunctions.

Key words:

• Sturm‐Liouville problem
• nonlocal two‐point condition
• positive eigenfunctions
• positive eigenvalues