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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, Number 5, Pages 17–21
(Mi ivm8995)
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This article is cited in 5 scientific papers (total in 5 papers)
On one inner theorem of uniqueness for linear elliptic second order equation with constant coefficients
I. A. Bikchantaev Chair of Differential Equations, Kazan (Volga Region) Federal University, 18 Kremlovskaya str., Kazan, 420008 Russia
Abstract:
We consider a linear elliptic second order differential equation. We prove that its solution $f$ is identical to zero if zeros of $f$ are condensed to two points along the non-collinear rays. We construct an example that shows that the requirement of non-collinearity of the rays is essential if the roots of the characteristic equation are distinct. In the case of equal roots of the characteristic equation this property will be true if and only if the rays do not belong to a straight line.
Keywords:
elliptic equation, uniqueness theorem.
Received: 13.12.2013
Citation:
I. A. Bikchantaev, “On one inner theorem of uniqueness for linear elliptic second order equation with constant coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5, 17–21; Russian Math. (Iz. VUZ), 59:5 (2015), 13–16
Linking options:
https://www.mathnet.ru/eng/ivm8995 https://www.mathnet.ru/eng/ivm/y2015/i5/p17
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Abstract page: | 151 | Full-text PDF : | 46 | References: | 38 | First page: | 11 |
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