Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 185, pp. 1-13.

Title: Oscillation of solutions to second-order nonlinear differential
       equations of generalized Euler type

Authors: Asadollah Aghajani (Iran Univ. of Science and Technology, Tehran, Iran)
         Donal O'Regan (National Univ. of Irland, Galway, Irland)
         Vahid Roomi   (Iran Univ. of Science and Technology, Tehran, Iran)

Abstract:
 We are concerned with the oscillatory behavior of the solutions of
 a generalized Euler differential 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
 sufficient  conditions and some explicit sufficient 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.


Submitted May 30, 2013. Published August 10, 2013.
Math Subject Classifications: 34C10, 34A12.
Key Words: Oscillation; nonlinear differential equations; Lienard system.