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Oscillation of second order semilinear elliptic equations with damping

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Abstract

We obtain some new Kamenev-type oscillation theorems for the second order semilinear elliptic differential equation with damping

$$ \sum\limits_{i,j = 1}^N {D\left[ {a_{ij} \left( x \right)D_j y} \right] + } \sum\limits_{i = 1}^N {b_i \left( x \right)D_i y + c\left( x \right)f\left( y \right) = 0} $$

under quite general assumptions. These results are extensions of the recent results of Sun [Sun, Y. G.: New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping. J. Math. Anal. Appl., 291, 341–351 (2004)] in a natural way. In particular, we do not impose any additional conditions on the damped functions b i (x) except the continuity. Several examples are given to illustrate the main results.

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  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, P. R. China

    Zhi Ting Xu

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  1. Zhi Ting Xu
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Correspondence to Zhi Ting Xu.

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Dedicated to Professor Lizhi Wen on the occasion of his 80th birthday

Supported by Natural Science Foundation of Guangdong Province (Grant No. 8451063101000730)

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Xu, Z.T. Oscillation of second order semilinear elliptic equations with damping. Acta. Math. Sin.-English Ser. 26, 2165–2178 (2010). https://doi.org/10.1007/s10114-010-8331-0

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