New Oscillation Results for a Nonlinear Generalization of Euler Differential Equation

In the present work the behavior of the solutions of a nonlinear generalization of Euler type equation will be considered. First, the equation will be transformed to an equivalent planar system. Then, the intersection of the solutions with the vertical isocline of the system will be proven. Some conditions will also be presented under which the positive semitrajectory of the system starting from a point on the characteristic curve does not tend to the origin. Finally, new sufficient conditions will be established ensuring oscillation of all solutions of this equation. Examples will also be provided to show the relevance of the main results.