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On nonlinear perturbations of linear second order elliptic boundary value problems

Published online by Cambridge University Press:  24 October 2008

P. M. Fitzpatrick
P. M. Fitzpatrick
Affiliation:
University of Maryland
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Abstract

Let Ω ⊆ n be open and bounded, with ∂Ω smooth. Sufficient conditions on f are given in order that for p > n, the equation

has a solution for every h ∈ Lp; L is a second order symmetric elliptic operator and B represents either the first, second or third boundary value problems. These conditions are in terms of the asymptotic behaviour of f, in its second variable, in relation to those λ for which there is a nontrivial solution of

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 143 - 157
Copyright
Copyright © Cambridge Philosophical Society 1978

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