Geodesic
Nonstandard Lagrangian Singularities and Asymptotic Eigenfunctions of the Degenerating Operator $-\frac{d}{dx}D(x)\frac{d}{dx}$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 83-99

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We express the asymptotic eigenfunctions of the operator $-\frac{d}{dx}D(x)\frac{d}{dx}$ that degenerates at the endpoints of an interval in terms of the modified Maslov canonical operator introduced in our previous studies. 
@article{TM_2019_306_a7,
     author = {S. Yu. Dobrokhotov and V. E. Nazaikinskii},
     title = {Nonstandard {Lagrangian} {Singularities} and {Asymptotic} {Eigenfunctions} of the {Degenerating} {Operator} $-\frac{d}{dx}D(x)\frac{d}{dx}$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--99},
     publisher = {mathdoc},
     volume = {306},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_306_a7/}
}
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S. Yu. Dobrokhotov; V. E. Nazaikinskii. Nonstandard Lagrangian Singularities and Asymptotic Eigenfunctions of the Degenerating Operator $-\frac{d}{dx}D(x)\frac{d}{dx}$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 83-99. http://geodesic.mathdoc.fr/item/TM_2019_306_a7/