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On a maximum principle for a class of fourth-order semilinear elliptic equations

Published online by Cambridge University Press:  14 February 2012

Philip W. Schaefer
Philip W. Schaefer
Affiliation:
Department of Mathematics, The University of Tennessee
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Synopsis

It is shown that Ф = | grad u |2–uΔu, where u is a solution of Δ2u+pf(u) = 0 in D, assumes its maximum value on the boundary of D. This principle leads one to a lower bound on the first eigenvalue in the non-linear Dirichlet eigenvalue problem and to the non-existence of solutions to this non-linear partial differential equation subject to certain zero boundaryconditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 319 - 323
Copyright
Copyright © Royal Society of Edinburgh 1977

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