Sturm-Liouville eigenproblems with an interior double pole
Copyright policy )Sturm-Liouville eigenproblems with an interior double pole
The paper concerns the selfadjoint Sturm-Liouville eigenproblem \(w''(x)+ p(x) w(x)= 0\), on \([a, b]\), \(w(a)= w(b)= 0\), where the function \(p\) has a double pole and two simple turning points. By using the asymptotic behaviour of Whittaker functions the asymptotic approximation for high order modes is obtained. Moreover, for the low order modes a construction of the solution is presented which is based on the Titchmarsh-Weyl \(m\)- function theory.
- University of Zimbabwe Zimbabwe
turning points, Sturm-Liouville theory, Whittaker functions, Titchmarsh-Weyl \(m\)-function theory, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, asymptotic approximation, selfadjoint Sturm-Liouville eigenproblem, interior poles
turning points, Sturm-Liouville theory, Whittaker functions, Titchmarsh-Weyl \(m\)-function theory, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, asymptotic approximation, selfadjoint Sturm-Liouville eigenproblem, interior poles
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