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ANNULUS CRITERIA FOR OSCILLATION OF SECOND ORDER DAMPED ELLIPTIC EQUATIONS
Xu, Zhiting Korean Mathematical Society 2010 대한수학회지 Vol.47 No.6
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 ${\int}_{\Omega(r0)}c(x)dx=-\infty$.
ANNULUS CRITERIA FOR OSCILLATION OF SECOND ORDER DAMPED ELLIPTIC EQUATIONS
Zhiting Xu 대한수학회 2010 대한수학회지 Vol.47 No.6
Some annulus oscillation criteria are established for the second order damped elliptic differential equation [수식]under quite general assumption that they are based on the information only on a sequence of annuluses of Ω(r0) rather than on the whole exterior domain Ω(r0). 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 Ω(r0) c(x)dx = −∞.
Oscillation of Second Order Nonlinear Elliptic Differential Equations
Xu, Zhiting Department of Mathematics 2006 Kyungpook mathematical journal Vol.46 No.1
By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.
Oscillation of Second Order Nonlinear Elliptic Differential Equations
XU, ZHITING 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.1
By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping ◁수식 삽입▷(원문을 참조하세요) are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.
Oscillation of Certain Second Order Damped Quasilinear Elliptic Equations via the Weighted Averages
XIA, YONG,XU, ZHITING 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.2
By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation □D_(i)(a_(ij)(x)||D_(y)||^(p-2)D_(j)y+<b(x),||D_(y)||^(p-2)D_(y)>+c(x)f(y) = 0, p>1. The obtained theorems include and improve some existing ones for the undamped half-linear partial differential equation and the semilinear elliptic equation.