International Journal of Functional Analysis, Operator Theory and Applications
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Abstract: We study the property for solutions of a
semi-linear elliptic equation in three dimensional Euclidean space. In our
previous paper, we have proved the doubling property and the strong unique
continuation for the solutions of a semi-linear elliptic differential equation.
In this paper, we shall show that the doubling property holds under weaker
assumption. And we show that the unique continuation theorem and estimate for the solutions hold as
corollaries of the doubling property of the solutions.
