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On a semilinear equation in ℝ2 involving bounded measures

Published online by Cambridge University Press:  14 November 2011

Juan L. Vazquez
Juan L. Vazquez
Affiliation:
División de Matemáticas, Universidad Autónoma de Madrid and School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.
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Synopsis

We study the semilinear equation –Δu + β(u) = f in ℝ2, where β is a continuous increasing real function with β(0) = 0 and f is a bounded Radon measure. We show the existence of a solution, which is unique in the appropriate class, provided that each of the point masses contained in f does not exceed some critical value denned in terms of the growth of (β at ∞ This condition is shown to be necessary for the existence of solutions, even locally. The one-dimensional situation is also discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 181 - 202
Copyright
Copyright © Royal Society of Edinburgh 1983

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