Electron. J. Diff. Equ., Vol. 2013 (2013), No. 185, pp. 1-13.

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

Asadollah Aghajani, Donal O'Regan, Vahid Roomi

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.

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Asadollah Aghajani
School of Mathematics, Iran University of Science and Technology
P.O. box 16846-13114
Narmak, Tehran, Iran
email: aghajani@iust.ac.ir, Tel +9821-73225491, Fax +9821-73225891
Donal O'Regan
School of Mathematics, Statistics and Applied Mathematics
National University of Irland, Galway, Irland
email: donal.oregan@nuigalway.ie, Tel +353091 524411, Fax +353091 525700
Vahid Roomi
School of Mathematics, Iran University of Science and Technology
Narmak, Tehran, Iran
email: roomi@iust.ac.ir

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