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Fite and Kamenev type oscillation criteria for second order elliptic equations

Zhiting Xu — 2007

Annales Polonici Mathematici

Fite and Kamenev type oscillation criteria for the second order nonlinear damped elliptic differential equation ∑ i , j = 1 N D i [ a i j ( x ) D j y ] + ∑ i = 1 N b i ( x ) D i y + p ( x ) f ( y ) = 0 are obtained. Our results are extensions of those for ordinary differential equations and improve some known oscillation criteria in the literature. Several examples are given to show the significance of the results.

On the oscillation of forced second order mixed-nonlinear elliptic equations

Zhiting Xu — 2010

Annales Polonici Mathematici

Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ d i v ( A ( x ) | | ∇ y | | p - 1 ∇ y ) + ⟨ b ( x ) , | | ∇ y | | p - 1 ∇ y ⟩ + C ( x , y ) = e ( x ) , ⎨ ⎩ C ( x , y ) = c ( x ) | y | p - 1 y + ∑ i = 1 m c i ( x ) | y | p i - 1 y under quite general conditions. These results are extensions of the recent results of Sun and Wong, [J. Math. Anal. Appl. 334 (2007)] and Zheng, Wang and Han [Appl. Math. Lett. 22 (2009)] for forced second order ordinary differential equations with mixed nonlinearities, and include some known oscillation results in the literature

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