Geodesic
On bifurcation intervals for nonlinear eigenvalue problems
Annales Polonici Mathematici, Tome 71 (1999) no. 1, pp. 39-46
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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.
DOI : 10.4064/ap-71-1-39-46
Keywords: bifurcation interval, symmetric operator, Sturm-Liouville problem, Dirichlet problem, Leray-Schauder degree, characteristic values 
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Jolanta Przybycin. On bifurcation intervals for nonlinear eigenvalue problems. Annales Polonici Mathematici, Tome 71 (1999) no. 1, pp. 39-46. doi: 10.4064/ap-71-1-39-46

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