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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An alternate variational principle for $ \Delta u-u+\mid u\mid \sp{r-1}{\rm sgn}\,u=0$


Author: Charles V. Coffman
Journal: Proc. Amer. Math. Soc. 87 (1983), 666-670
MSC: Primary 35J60; Secondary 35J20
MathSciNet review: 687637
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Abstract: An alternate variational principle for the equation in the title has been proposed by H. A. Levine. We analyse the relation between this principle and the Rayleigh quotient that has been used previously for the variational study of this problem in $ {R^N}$. The main result is an existence theorem for $ {W^{1,2}}({R^N})$-solutions of the variational problem posed by Levine.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687637-X
PII: S 0002-9939(1983)0687637-X
Keywords: Variational principle, nonlinear elliptic boundary value problem
Article copyright: © Copyright 1983 American Mathematical Society