Oscillation of second order nonhomogeneous differential equations

This work concerns the linear, second order nonhomogeneous differential equation (NH) (r(x)y')' + q(x)y = f(x) and the associated homogeneous equation (H) (r(x)u')' + q(x)u = 0 . Necessary and sufficient conditions for solutions of (NH) to be oscillatory are given and separation theorems for solutions of (H) and (NH) are established. Asymptotic behavior of (NH) is studied and the structure of the solution space of (NH) is determined. A polar coordinate transformation for (NH) is obtained and two-point boundary problems are solved for (NH) when a parameter is involved.