Geodesic
Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 187-207 
A. Yu. Kolesov; E. F. Mishchenko; N. Kh. Rozov. Solution to Singularly Perturbed Boundary Value Problems by the Duck Hunting Method. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 187-207. http://geodesic.mathdoc.fr/item/TM_1999_224_a11/
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     author = {A. Yu. Kolesov and E. F. Mishchenko and N. Kh. Rozov},
     title = {Solution to {Singularly} {Perturbed} {Boundary} {Value} {Problems} by the {Duck} {Hunting} {Method}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A situation is analyzed when two different curves of slow motion intersect in a general way in a two-dimensional relaxation system. It is shown that this situation gives rise to the so-called duck trajectories. The results of the analysis are applied to the construction of the asymptotics of the principal eigenvalue of the Dirichlet problem for a singularly perturbed Schrödinger equation.

[1] Pontryagin L. S., Mischenko E. F., Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkie k razryvnym, Preprint, Mekh.-mat. fak. MGU, M., 1955, 5 pp.

[2] Mischenko E. F., Pontryagin L. S., “Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkie k razryvnym”, DAN SSSR, 102:5 (1955), 889–891

[3] Pontryagin L. S., “Sistemy obyknovennykh differentsialnykh uravnenii s malymi parametrami pri vysshikh proizvodnykh”, Tr. 3-go Vsesoyuz. mat. s'ezda, t. 3, Izd-vo AN SSSR, M., 1958, 570–577

[4] Pontryagin L. S., “Asimptoticheskoe povedenie reshenii sistem differentsialnykh uravnenii s malym parametrom pri vysshikh proizvodnykh”, Izv. AN SSSR. Ser. mat., 21:5 (1957), 605–626 | MR | Zbl

[5] Mischenko E. F., “Asimptoticheskoe vychislenie periodicheskikh reshenii sistem differentsialnykh uravnenii, soderzhaschikh malye parametry pri proizvodnykh”, Izv. AN SSSR. Ser. mat., 21:5 (1957), 627–654

[6] Mischenko E. F., Rozov N. Kh., Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Nauka, M., 1975 | MR

[7] Mischenko E. F., Kolesov Yu. S., Kolesov A. Yu., Rozov N. Kh., Periodicheskie dvizheniya i bifurkatsionnye protsessy v singulyarno vozmuschennykh sistemakh, Fizmatlit, M., 1995 | MR

[8] Zvonkin A. K., Shubin M. A., “Nestandartnyi analiz i singulyarnye vozmuscheniya obyknovennykh differentsialnykh uravnenii”, UMN, 39:2 (1984), 77–127 | MR | Zbl

[9] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[10] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969 | MR | Zbl

[11] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, Izd-vo inostr. lit., M., 1958

[12] Kolesov Yu. S., Chaplygin V. F., “O neostsillyatsii reshenii singulyarno vozmuschennykh uravnenii vtorogo poryadka”, DAN SSSR, 199:6 (1971), 1240–1242 | MR