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On the bifurcation theory of semilinear elliptic eigenvalue problems

Author: Charles V. Coffman
Journal: Proc. Amer. Math. Soc. 31 (1972), 170-176
MSC: Primary 35P99
MathSciNet review: 0306733
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Abstract: A standard ``bootstrap'' method is used to show that the bifurcation problem for the semilinear eigenvalue problem $ \Delta u + \lambda f(x,u) = 0$ in $ \Omega $, $ u{\vert _{\partial \Omega }} = 0$, where $ f(x,0) \equiv 0$, and $ (\partial /\partial u)f(x,0) > 0$, and when formulated in terms of weak solutions, is a local problem, i.e. independent of the behavior of $ f$ for large $ u$. A principle of linearization for this problem is proved under mild differentiability conditions on $ f$.

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Keywords: Bifurcation theory, bifurcation point, principle of linearization, "bootstrap'' method, integral equation
Article copyright: © Copyright 1972 American Mathematical Society

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