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Abstract
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In this paper the generalized nonlinear Euler differential equation t2k(tu′)u″ + t(f(u)+ k(tu′))u′ + g(u) = 0 is
considered. Here the functions f(u), g(u) and k(u) satisfy smoothness conditions which guarantee the
uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are
assumed. We present some necessary and sufficient conditions and some tests for the equivalent planar
system to have or fail to have property (X+), which is very important for the existence of periodic solutions
and oscillation theory.
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