Generalization of the boundary function method for solving boundary-value problems for bisingularly perturbed second-order differential equations (Q2436380)

The authors consider a bisingular boundary value problem of the form \[ \varepsilon y''(x) + x y'(x) - q(x) y(x) = f(x),\quad x\in[0,1],\qquad y(0) = 0,\quad y(1) = y^0, \eqno{(*)} \] where \(\varepsilon > 0\) is a small parameter, \(y^0\in\mathbb{R}\) is a given constant, and \(q(x)\) and \(f(x)\) are analytic functions such that \(q(x) \geq 1\) and \(q(0) = 1\). Using the boundary function method they construct an asymptotics of the solution to problem (\(*\)), which apparently has a simpler structure than the asymptotics constructed earlier by the matching asymptotics method.