Geodesic
Asymptotic solution of first-order equation with small parameter under the derivative with perturbed operator
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 784-796

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The paper is devoted to the Cauchy problem for a differential equation with a small parameter when using a Fredholm operator in a Banach space with a certain method. The investigated effect of this parameter. The solution is in the form of an asymptotic expansion. When solving the problems of using the cascade decomposition method for equations, which allows us to split the equation into equations in subspaces.
Keywords: differential equation, asymptotic solution, small parameter, perturbation in the right-hand side, Fredholm operator, boundary layer phenomenon. 
@article{VTAMU_2018_23_124_a21,
     author = {V. I. Uskov},
     title = {Asymptotic solution of first-order equation with small parameter under the derivative with perturbed operator},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {784--796},
     publisher = {mathdoc},
     volume = {23},
     number = {124},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a21/}
}
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V. I. Uskov. Asymptotic solution of first-order equation with small parameter under the derivative with perturbed operator. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 124, pp. 784-796. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_124_a21/