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Global bifurcation analysis and uniqueness for a semilinear problem

Published online by Cambridge University Press:  14 November 2011

Achilles Tertikas
Achilles Tertikas
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, U.K.
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Synopsis

We study the bifurcation diagram and uniqueness of solutions of

By using a rescaling technique and the Implicit Function Theorem, we establish the global bifurcation diagram. Uniqueness is proved by a separation argument to complete the bifurcation picture of the problem. Our study suggests that the bifurcation diagrams have different behaviour at λ = 0, depending on whether g(∞) > 0 or g(∞) < 0 in L∞ norm, but quite similar behaviour in Lp or W2,1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 3-4 , 1989 , pp. 265 - 284
Copyright
Copyright © Royal Society of Edinburgh 1989

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