Geodesic
A note on the characterisation of eigencurves for certain two parameter eigenvalue problems in ordinary differential equations
Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 63-67

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We are interested in two parameter eigenvalue problems of the formsubject to Dirichlet boundary conditionsThe weight function 5 and the potential q will both be assumed to lie in L2[0,1]. The problem (1.1), (1.2) generates eigencurvesin the sense that for any fixed λ, ν(λ) is the nth eigenvalue ν, (according to oscillation indexing) of (1.1), (1.2). These curves are in fact analytic functions of λ and have been the object of considerable study in recent years. The survey paper [1] provides background in this area and itemises properties of eigencurves. 
Browne, Patrick J.; Sleeman, B. D. A note on the characterisation of eigencurves for certain two parameter eigenvalue problems in ordinary differential equations. Glasgow mathematical journal, Tome 35 (1993) no. 1, pp. 63-67. doi: 10.1017/S0017089500009563
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[1] 1.Browne, P. J., Two parameter eigencurve theory, in Ordinary and Partial Differential Equations Vol. II, Pitman Research Notes in Mathematics No. 216, (Longman, 1989), 52–60. Google Scholar

[2] 2.Poschel, J. and Trubowitz, E., Inverse spectral theory, (Academic Press, 1987). Google Scholar

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