The Behavior of the Solutions of Delta U = F(x, U) In the Neighborhood of a Point (Classic Reprint)

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Excerpt from The Behavior of the Solutions of Delta U = F(x, U) In the Neighborhood of a PointThus in this paper it is proved that any solution of (2) that vanishes more strongly than any power vanishes identically. Until now this result has been proved in p dimensions only with the assumption that k2(x) be analytic in (x). A result similar to Theorem II was proved by T. Carleman[1] for two dimensions, but his method cannot be extended to higher dimensions. It seems therefore that the method developed below is the first to give results on the local behavior of the solutions of a general class of nonanalytic differential equations in any number of variables.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.