Geodesic
Asymptotic Formulae for the Eigenvalues of a Two Parameter System of Ordinary Differential Equations of the Second Order
Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 657-665

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The origin and importance of multiparameter Sturm-Liouville problems in mathematical physics has recently been discussed by Atkinson [1, sects. 3 and 4], [2, introduction]. In spite of the importance of such problems, and in spite of the work done in this field by such early investigators as Klein and Hilbert, Atkinson points out that in recent years this field has been relatively neglected in contrast to the single parameter case. As an example, he states that as opposed to the one parameter case, the detailed behaviour of the eigenvalues and eigenfunctions in the multiparameter Sturm-Liouville case is still far from clear. 
Faierman, M. Asymptotic Formulae for the Eigenvalues of a Two Parameter System of Ordinary Differential Equations of the Second Order. Canadian mathematical bulletin, Tome 17 (1975) no. 5, pp. 657-665. doi: 10.4153/CMB-1974-119-0
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     author = {Faierman, M.},
     title = {Asymptotic {Formulae} for the {Eigenvalues} of a {Two} {Parameter} {System} of {Ordinary} {Differential} {Equations} of the {Second} {Order}},
     journal = {Canadian mathematical bulletin},
     pages = {657--665},
     year = {1975},
     volume = {17},
     number = {5},
     doi = {10.4153/CMB-1974-119-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-119-0/}
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