The asymptotic solution of the three-band bisingularly problem

Abstract

The paper proposes an analogue of Vishik–Lyusternik–Vasileva–Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to many band (or with an intermediate boundary layers) bisingularly problems. By means of this method we construct the uniform asymptotic expansion for the solution to the three-band bisingular Dirichlet problem for second order ordinary differential equation on the interval. By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established.