Asymptotic behavior of the curves in the Fu{v{c}}{\'{i}}k spectrum

In this work we study the asymptotic behavior of the curves of the Fu{\v{c}}{\'{\i}}k spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fu{\v{c}}{\'{\i}}k spectrum with rays through the origin, and we compare their values with the asymptotic ones.