Geodesic
Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 5, pp. 682-710

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a linear differential equation of second order with a small factor at the highest derivative. We study the problem of the asymptotic behavior of the eigenvalues of the first boundary value problem (task Dirichlet) in situation when the turning points (points where the coefficient at the first derivative equals to zero) exist. It is shown that only the behavior of coefficients of the equation in a small neighborhood of the turning points is essential. The main result is a theorem on the limit values of the eigenvalues of the first boundary value problem.
Keywords: singularly perturbed equation, turning points, asymptotic, boundary value problem, eigenvalues. 
@article{MAIS_2015_22_5_a5,
     author = {S. A. Kaschenko},
     title = {Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {682--710},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2015_22_5_a5/}
}
TY  - JOUR
AU  - S. A. Kaschenko
TI  - Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2015
SP  - 682
EP  - 710
VL  - 22
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2015_22_5_a5/
LA  - ru
ID  - MAIS_2015_22_5_a5
ER  - 
%0 Journal Article
%A S. A. Kaschenko
%T Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points
%J Modelirovanie i analiz informacionnyh sistem
%D 2015
%P 682-710
%V 22
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2015_22_5_a5/
%G ru
%F MAIS_2015_22_5_a5
S. A. Kaschenko. Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 5, pp. 682-710. http://geodesic.mathdoc.fr/item/MAIS_2015_22_5_a5/