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http://dx.doi.org/10.14317/jami.2011.29.5_6.1557

OSCILLATION THEOREMS FOR CERTAIN SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS  

Sun, Yibing (School of Science, University of Jinan)
Han, Zhenlai (School of Science, University of Jinan, School of Control Science and Engineering, Shandong University)
Zhao, Ping (School of Control Science and Engineering, University of Jinan)
Sun, Ying (School of Science, University of Jinan)
Publication Information
Journal of applied mathematics & informatics / v.29, no.5_6, 2011 , pp. 1557-1569 More about this Journal
Abstract
In this paper, we consider the oscillation of the following certain second order nonlinear differential equations $(r(t)(x^{\prime}(t))^{\alpha})^{\prime}+q(t)x^{\beta}(t)=0$>, where ${\alpha}$ and ${\beta}$ are ratios of positive odd integers. New oscillation theorems are established, which are based on a class of new functions ${\Phi}={\Phi}(t,s,l)$ defined in the sequel. Also, we establish some interval oscillation criteria for this equation.
Keywords
Oscillation; Second order nonlinear differential equations; Interval criteria; Riccati transformation technique;
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