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

Positive eigenvalues and corresponding eigenfunctions of the linear Sturm-Liouville problem with one classical boundary condition and another non- local two-point boundary condition are considered in this paper. Four cases of non- local two-point boundary conditions are analysed. We get positive eigenfunctions existence domain for each case of these problems. This domain depends on the pa- rameters of the nonlocal boundary problem and it gives necessary and sufficient conditions for existing positive eigenvalues with positive eigenfunctionsMatematikos ir informatikos institutasVytauto Didžiojo universiteta