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Teoreticheskaya i Matematicheskaya Fizika, 1978, Volume 34, Number 1, Pages 15–22
(Mi tmf2676)
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This article is cited in 5 scientific papers (total in 5 papers)
Classical equations of Euclidean field theory
I. V. Volovich
Abstract:
A study is made of the nonlinear elliptic equation $\Delta u=F(u)+f(x)$ in the whole of the space $R^n$. It is shown that if the function $f(x)$ has compact support and $F(u)$ satisfies the conditions $F(0)=0$, $F'(u)\geqslant\varkappa^2>0$, where $\varkappa$ is a constant, then a classical
solution of this equation in the class of bounded functions exists, is unique, and decreases exponentially at infinity. Some cases when the condition $F'(u)\geqslant\varkappa^2$ is not satisfied are also considered. In particular, it is shown for the Goldstone model that at least two bounded solutions exist.
Received: 12.05.1977
Citation:
I. V. Volovich, “Classical equations of Euclidean field theory”, TMF, 34:1 (1978), 15–22; Theoret. and Math. Phys., 34:1 (1978), 9–14
Linking options:
https://www.mathnet.ru/eng/tmf2676 https://www.mathnet.ru/eng/tmf/v34/i1/p15
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Abstract page: | 484 | Full-text PDF : | 134 | References: | 73 | First page: | 3 |
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