Asymptotics of eigenvalues of first boundary value problem for singularly pertubed second-order differential equation with turning points

We consider a linear differential equation of second order with a small factor at the highest derivative. We study the problem of the asymptotic behavior of the eigenvalues of the first boundary value problem (task Dirichlet) in situation when the turning points (points where the coefficient at the first derivative equals to zero) exist. It is shown that only the behavior of coefficients of the equation in a small neighborhood of the turning points is essential. The main result is a theorem on the limit values of the eigenvalues of the first boundary value problem.