New Kamenev-type oscillation criteria for half-linear partial differential equations |
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Authors: | Ge-feng Yang Zhi-ting Xu |
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Institution: | 1. Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou, 510006, China 2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
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Abstract: | We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping (E) $div(A(x)\left\| {\nabla u} \right\|^{p - 2} \nabla u) + \left\langle {b(x),\left\| {\nabla u} \right\|^{p - 2} \nabla u} \right\rangle + c(x)\left| u \right|^{p - 2} u = 0$ under quite general conditions. These results are extensions of the recent results developed by Sun Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341–351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. |
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Keywords: | oscillation half-linear partial differential equations Kamenev-type Damped equation |
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