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Global bifurcation analysis and uniqueness for a semilinear problem
Published online by Cambridge University Press: 14 November 2011
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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