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Asymptotic Properties of Semilinear Equations

Published online by Cambridge University Press:  20 November 2018

Allan L. Edelson
Allan L. Edelson*
Affiliation:
Department of Mathematics, University of California, Davis, California 95616
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Abstract

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We study the asymptotic properties of positive solutions to the semilinear equation — Δu = f(x, u). Existence and asymptotic estimates are obtained for solutions in exterior domains, as well as entire solutions, for n ≧ 2. The study uses integral operator equations in Rn, and convergence theorems for solutions of Poisson's equation in bounded domains. A consequence of the method is that more precise estimates can be obtained for the growth of solutions at infinity, than have been obtained by other methods. As a special case the results are applied to the generalized Emden-Fowler equation — Δu = p(x)uγ, for γ > 0

Keywords

34C1034C1134D10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 34 - 46
Copyright
Copyright © Canadian Mathematical Society 1989

References

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