Article contents
Asymptotic Properties of Semilinear Equations
Published online by Cambridge University Press: 20 November 2018
Abstract
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
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1989
References
- 9
- Cited by