The finite spectrum of Sturm-Liouville problems with transmission conditions and eigenparameter-dependent boundary conditions. (English) Zbl 1280.34029

The authors study a Sturm-Liouville equation of the form \[ -(py')'+qy=\lambda wy\text{ for } x\in (a,c)\cup(c,b), \] where \(c\in(a,b)\), \(-\infty<a<b<+\infty\), under eigenparameter-dependent boundary conditions and transmission conditions. For any positive integers \(m\) and \(n\), the authors construct a class of problems which have at most \(m+n+4\) eigenvalues.


34B24 Sturm-Liouville theory
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L05 General spectral theory of ordinary differential operators
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