In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral typewhere), α > 0 and β > 0 are established. Our results improve some well-known results which were published recently in the literature. Some illustrating examples are also provided to show the importance of our results.
The study of the oscillatory behavior of solutions to second order nonlinear differential equations is motivated by their numerous applications in the natural sciences and engineering. In the presented research, some new oscillation criteria for a class of damped second order neutral differential equations with noncanonical operators are established. The results extend and improve on those reported in the literature. Moreover, some examples are provided to show the significance of the results.
We study the oscillatory behavior of solution to the second order nonlinear differential equations with a sub-linear neutral term $$ \big(a(t)[(x(t)+p(t)x^{\alpha}(\tau(t)))']^{\gamma}\big)'+q(t)x^{\beta}(\sigma(t))=0, \quad t\geq t_0>0. $$ A new criterion is established that improves related results reported in the literature. Moreover, some examples are provided to illustrate the main results.
By studying the nonlinear functional equation with variable coefficientsthe oscillation of the solution in this paper, we reached some new oscillation criterion.
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