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

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Xu Z.

Annales Polonici Mathematici

2010

tom 98

nr 2

169-188

Oscillation theorems are established for forced second order mixed-nonlinear elliptic differential equations ⎧ $div(A(x)||∇y||^{p-1}∇y) + ⟨b(x),||∇y||^{p-1}∇y⟩ + C(x,y) = e(x)$, ⎨ ⎩ $C(x,y) = c(x)|y|^{p-1}y + ∑_{i=1}^m c_i(x)|y|^{p_i-1}y}$ 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

Fite and Kamenev type oscillation criteria for second order elliptic equations

100%

Xu Z.

Annales Polonici Mathematici

2007

tom 92

nr 3

199-214

Fite and Kamenev type oscillation criteria for the second order nonlinear damped elliptic differential equation $∑_{i,j=1}^N D_i[a_{ij}(x)D_j y] + ∑_{i=1}^Nb_i(x)D_iy + p(x)f(y) = 0$ 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.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Xu Z.

1 2010

1 2007

Wyniki wyszukiwania

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

Fite and Kamenev type oscillation criteria for second order elliptic equations