I've read for a regular Sturm-Liouville problem for each eigenvalue there corresponds unique eigenfunction. For periodic Sturm Liouville problem Which of the following are true? Each eigenvalue of (periodic Sturm Liouville problem) corresponds to 1. one eigenfunction 2. two eigenfunctions 3. two linearly independent eigenfunctions 4. two orthogonal eigenfunctions What are the Properties of eigenvalues and eigenfunctions of periodic Sturm Liouville problem? Are these depend on boundary conditions or same for all periodic Sturm Liouville problems?
What are the Properties of eigenvalues and eigenfunctions of periodic Sturm Liouville problem?
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ordinary-differential-equations
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0This is addressed thoroughly in Coddington-Levinson's *Theory of ODEs*, chapter 8, section 3. – 2012-04-26