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eigenvalue asymptotics

Proceedings of the Edinburgh Mathematical Society (1)

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STURM–LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS RATIONALLY DEPENDENT ON THE EIGENPARAMETER. I
Paul A. Binding, Patrick J. Browne, Bruce A. Watson
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 3 / October 2002

Published online by Cambridge University Press:

14 October 2002, pp. 631-645
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We consider the Sturm–Liouville equation
$$ -y''+qy=\lambda y\quad\text{on }[0,1], $$
subject to the boundary conditions
$$ y(0)\cos\alpha=y'(0)\sin\alpha,\quad\alpha\in[0,\pi), $$
and
$$\frac{y'}{y}(1)=a\lambda+b-\sum_{k=1}^N\frac{b_k}{\lambda-c_k}. $$
Topics treated include existence and asymptotics of eigenvalues, oscillation of eigenfunctions, and transformations between such problems.
AMS 2000 Mathematics subject classification: Primary 34B24; 34L20