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Nonexistence of local minima of supersolutions for the polyharmonic problems

✍ Scribed by Liangpan Li

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
89 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this note we study the nonexistence of local minima of the supersolutions of the polyharmonic equations on the balls under generalized homogeneous Dirichlet boundary conditions. Under suitable restriction on the dimensions, this means that a generalized clamped circular plate, which is pushed from below, cannot bend downwards even locally. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is