Classical equations of Euclidean field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 15-22
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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.
@article{TMF_1978_34_1_a1,
author = {I. V. Volovich},
title = {Classical equations of {Euclidean} field theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {15--22},
publisher = {mathdoc},
volume = {34},
number = {1},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1978_34_1_a1/}
}
I. V. Volovich. Classical equations of Euclidean field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 34 (1978) no. 1, pp. 15-22. http://geodesic.mathdoc.fr/item/TMF_1978_34_1_a1/