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  • Proceedings of the Edinburgh Mathematical Society, Volume 37, Issue 1
  • February 1994, pp. 57-72

Sturm–Liouville problems with eigenparameter dependent boundary conditions

  • P. A. Binding (a1), P. J. Browne (a2) and K. Seddighi (a3)
  • DOI: http://dx.doi.org/10.1017/S0013091500018691
  • Published online: 01 January 2009
Abstract

Sturm theory is extended to the equation

for 1/p, q, rL1 [0, 1] with p, r > 0, subject to boundary conditions

and

Oscillation and comparison results are given, and asymptotic estimates are developed. Interlacing of eigenvalues with those of a standard Sturm–Liouville problem where the boundary conditions are ajy(j) = cj(py′)(j), j=0, 1, forms a key tool.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

6.D. B. Hinton , An expansion theorem for an eigenvalue problem with eigenvalue in the boundary condition, Quart. J. Math. Oxford, 30 (1979), 3342.

11.W. T. Reid , Sturmian Theory for Ordinary Differential Equations (Springer-Verlag, 1980).

12.J. Walter , Regular eigenvalue problems with eigenvalue parameter in the boundary conditions, Math. Z., 133 (1973), 301312.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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