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# Abstract linear second order differential equations with two small parameters and depending on time operators

### Abstract

carpathian_2017_33_2_233_246_abstract

Issue no:

In a real Hilbert space consider the following singularly perturbed Cauchy problem

where is a family of linear self-adjoint
operators, , and
are two small parameters. We study the behavior of solutions to this problem
in two different cases: and and , relative to solution to the corresponding unperturbed problem.We obtain some {\it a priori} estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of We show the boundary layer and boundary layer function in both cases.