Geodesic
On a Non-Analytic Perturbation Problem
Canadian mathematical bulletin, Tome 4 (1961) no. 3, pp. 243-248

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The purpose here is to study a type of perturbation problem, arising from a differential equation, which is not included in the realm of analytic or asymptotic perturbation theory [4], [6]. Such a problem arises when the domain of the differential operator has been subjected to a variation (rather than the formal operator). We propose to outline one simple problem of this type, concerned with a second order ordinary differential operator. Our purpose is to obtain asymptotic estimates for the characteristic values of a regular Sturm-Liouville problem on a closed interval [a, b] when b is near a singular point of the differential operator. Similar results have been obtained in [3], [8], and [9] by other methods. 
Swanson, C. A. On a Non-Analytic Perturbation Problem. Canadian mathematical bulletin, Tome 4 (1961) no. 3, pp. 243-248. doi: 10.4153/CMB-1961-027-6
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     author = {Swanson, C. A.},
     title = {On a {Non-Analytic} {Perturbation} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {243--248},
     year = {1961},
     volume = {4},
     number = {3},
     doi = {10.4153/CMB-1961-027-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1961-027-6/}
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