ON THE OSCILLATION OF AN ELLIPTIC EQUATION OF FOURTH ORDER
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Abstract
The elliptic equation
\[\Delta^2 u(|x|)+g(|x|)u(|x|)=f(|x|)\]
is studied for its oscillatory behavior. $\Delta$ is the Laplace operator. Sufficient condi tions have been found to ensure that all solutions of this equation continuable in some exterior domain $\Omega=\{x=(x_1, x_2, x_3):|x|>A\}$ where $|x|=(\sum_{i=1}^3 x_i^2)^{1/2}$ are oscillatory.
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