Linear Sturm–Liouville problems with general homogeneous linear multi‐point boundary conditions
Copyright policy )Linear Sturm–Liouville problems with general homogeneous linear multi‐point boundary conditions
In this paper, we study second order linear Sturm–Liouville problems involving one or two homogeneous linear multi‐point boundary conditions in the most general form. We obtain conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Furthermore, we reveal the interlacing relations between the eigenvalues of such Sturm–Liouville problems and those of Sturm–Liouville problems with certain two‐point separated boundary conditions.
- Northwestern University United States
- Carroll College United States
- Northern Illinois University United States
Sturm-Liouville theory, Nonlinear boundary value problems for ordinary differential equations, multi-point boundary conditions, matching method, eigenvalues, Linear boundary value problems for ordinary differential equations, Boundary eigenvalue problems for ordinary differential equations, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, nodal solutions, Nonlocal and multipoint boundary value problems for ordinary differential equations, Sturm-Liouville problems
Sturm-Liouville theory, Nonlinear boundary value problems for ordinary differential equations, multi-point boundary conditions, matching method, eigenvalues, Linear boundary value problems for ordinary differential equations, Boundary eigenvalue problems for ordinary differential equations, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, nodal solutions, Nonlocal and multipoint boundary value problems for ordinary differential equations, Sturm-Liouville problems
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