Linear Sturm‐Liouville problems with multi‐point boundary conditions
Copyright policy )Linear Sturm‐Liouville problems with multi‐point boundary conditions
AbstractWe study second order linear Sturm‐Liouville problems which involve one or two multi‐point boundary conditions. Conditions for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions are derived. We also show that these eigenvalues are algebraically simple. Moreover, we obtain certain interlacing relations between the eigenvalues of Sturm‐Liouville problems with multi‐point boundary conditions and those with two‐point separated boundary conditions. The work for multi‐point Sturm‐Liouville problems will set up a foundation for the further studies of nonlinear boundary value problems with multi‐point boundary conditions.
- City University of Hong Kong China (People's Republic of)
- University of Hong Kong China (People's Republic of)
- Northwestern University United States
- Hong Kong Polytechnic University China (People's Republic of)
- Northern Illinois University United States
Sturm-Liouville theory, multi-point boundary conditions, interlacing of eigenvalues, eigenvalue multiplicity, Boundary eigenvalue problems for ordinary differential equations, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Nonlocal and multipoint boundary value problems for ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
Sturm-Liouville theory, multi-point boundary conditions, interlacing of eigenvalues, eigenvalue multiplicity, Boundary eigenvalue problems for ordinary differential equations, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Nonlocal and multipoint boundary value problems for ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
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