Asymptotic Expansions of Eigenvalues of the First Boundary Problem for Singularly Perturbed Second Order Diﬀerential Equation with Turning Points - S. A. Kashchenko (Моделирование и анализ информационных систем, 2016)
For singularly perturbed second order equations the dependence of eigenvalues of the ﬁrst boundary problem on a small parameter at the highest derivative is studied. The main assumption is that the coeﬃcient at the ﬁrst derivative in the equation is the sign of the variable. This leads to the emerging of so-called turning points. Asymptotic expansions on the small parameter are obtained for all eigenvalues of the considered boundary problem. It turns out that the expansions are deﬁned by the behavior of coeﬃcients in a neighborhood of turning points only