Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Sturm–Liouville problems with eigenparameter dependent boundary conditions

P. A. Bindinga1*, P. J. Brownea2* and K. Seddighia3

a1 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, Canada

a2 Department of Mathematics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0W0, Canada

a3 Department of Mathematics, University of Shiraz, Iran 71454

Abstract

Sturm theory is extended to the equation

S0013091500018691_eqnU1

for 1/p, q, rxs2208L1 [0, 1] with p, r > 0, subject to boundary conditions

S0013091500018691_eqnU2

and

S0013091500018691_eqnU3

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.

(Received June 26 1992)

Footnotes

* Research support in part by grants from the NSERC of Canada.