Sturm theorems for second order linear nonhomogenous differential equations and localization of zeros of the solution

Abstract

It is shown that Sturm theorems, formulated in the 1830’s ([1], [2], [3] and [4]) and valid for second order linear homogeneous differential equation L(y)≡y″+a(x)y′+b(x)y=0, could as well be formulated for the class of nonhomogeneous linear differential equations L(y)=f(x). Criteria for the existence of oscillatory solutions of nonhomogeneous equations, as well as more exact locations of the zeros are given.