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An analytical study of bifurcation problems for equations involving Fredholm mappings

Published online by Cambridge University Press:  14 November 2011

N.X. Tan
N.X. Tan
Affiliation:
Karl-Weierstraß-Institut für Mathematik der Akademie der Wissenschaften der DDR, Mohrenstraße 39, 1086 Berlin, DDR Institute of Mathematics, Hanoi Vietnam Box 631, Buu Dien BO HO, Hanoi, Vietnam
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Extract

Let us consider equations in the form

where Λ is an open subset of a normed space. For any fixed λ ∊ Λ, T, L(λ,.) and M(λ,.) are mappings from the closure D0 of a neighbourhood D0 of the origin in a Banach space X into another Banach space Y with T(0) = L(λ, 0) = M(λ, 0) = 0. Let λ be a characteristic value of the pair (T, L) such that T − L(λ,.) is a Fredholm mapping with nullity p and index s, p> s≧ 0. Under sufficient hypotheses on T, L and M, (λ, 0) is a bifurcation point of the above equations. Some well-known results obtained by Crandall and Rabinowitz [2], McLeod and Sattinger [5] and others will be generalised. The results in this paper are extensions of the results obtained by the author in [7].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 199 - 225
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

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