ArticleOriginal scientific text
Title
On bifurcation intervals for nonlinear eigenvalue problems
Authors 1
Affiliations
- Department of Applied Mathematics, University of Mining and Metallurgy, Mickiewicza 30, 30-059 Kraków, Poland
Abstract
We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity.
Keywords
bifurcation interval, symmetric operator, Sturm-Liouville problem, Dirichlet problem, Leray-Schauder degree, characteristic values
Bibliography
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Pages:
39-46
Main language of publication
English
Received
1998-02-23
Accepted
1998-10-14
Published
1999
Exact and natural sciences