Geodesic
On a~method of construction of asymptotic decompositions of bisingular perturbed problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 3-11

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We propose an analog of the method of boundary functions for constructing uniform asymptotic expansions of solutions to bisingular perturbed problems. With the use of this method we construct uniform asymptotic expansions of solutions to the Dirichlet problem for bisingular perturbed ordinary differential equations and second order elliptic equations. Applying the maximum principle, we obtain estimates for the remainder terms.
Keywords: asymptotic expansion, Dirichlet problem, Airy function, boundary functions. 
@article{IVM_2016_12_a0,
     author = {K. Alymkulov and D. A. Tursunov},
     title = {On a~method of construction of asymptotic decompositions of bisingular perturbed problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--11},
     publisher = {mathdoc},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_12_a0/}
}
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K. Alymkulov; D. A. Tursunov. On a~method of construction of asymptotic decompositions of bisingular perturbed problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2016_12_a0/