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Abstract
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We are concerned with the oscillatory behavior of the solutions
of a generalized Euler diferential equation where the nonlinearities satisfy
smoothness conditions which guarantee the uniqueness of solutions of initial
value problems, however, no conditions of sub(super) linearity are assumed.
Some implicit necessary and suffcient conditions and some explicit suffcient
conditions are given for all nontrivial solutions of this equation to be oscillatory
or nonoscillatory. Also, it is proved that solutions of the equation are all
oscillatory or all nonoscillatory and cannot be both.
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