مشخصات پژوهش

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.