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ANNULUS CRITERIA FOR OSCILLATION OF SECOND ORDER DAMPED ELLIPTIC EQUATIONS

  • Xu, Zhiting
  • Received : 2009.02.16
  • Published : 2010.11.01

Abstract

Some annulus oscillation criteria are established for the second order damped elliptic differential equation $$\sum\limits_{i,j=1}^N D_i[a_{ij}(x)D_jy]+\sum\limits_{i=1}^Nb_i(x)D_iy+C(x,y)=0$$ under quite general assumption that they are based on the information only on a sequence of annuluses of $\Omega(r_0)$ rather than on the whole exterior domain $\Omega(r_0)$. Our results are extensions of those due to Kong for ordinary differential equations. In particular, the results obtained here can be applied to the extreme case such as ${\int}_{\Omega(r0)}c(x)dx=-\infty$.

Keywords

oscillation;annulus criteria;elliptic equations;second order;damped

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