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Abstract
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In the present work the behavior of the solutions of a nonlinear gener-
alization 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.
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