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
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.
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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
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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
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Vahid Roomi
School of Mathematics, Iran University of Science and Technology
Narmak, Tehran, Iran
email: roomi@iust.ac.ir
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