Geodesic
Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 1, pp. 41-60

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For singularly perturbed second order equations the dependence of eigenvalues of the first boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coefficient at the first derivative in the equation is the sign of the variable. This leads to the emerging of so-called turning points. Asymptotic expansions on the small parameter are obtained for all eigenvalues of the considered boundary problem. It turns out that the expansions are defined by the behavior of coefficients in a neighborhood of turning points only.
Keywords: singularly perturbed equation, turning points, asymptotic, boundary value problem, eigenvalues. 
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     author = {S. A. Kashchenko},
     title = {Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {41--60},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_1_a3/}
}
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S. A. Kashchenko. Asymptotic expansions of eigenvalues of the first boundary problem for singularly perturbed second order differential equation with turning points. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 1, pp. 41-60. http://geodesic.mathdoc.fr/item/MAIS_2016_23_1_a3/