On bifurcation intervals for nonlinear eigenvalue problems

• Autorzy: Jolanta Przybycin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

bifurcation interval; symmetric operator; Sturm-Liouville problem; Dirichlet problem; Leray-Schauder degree; characteristic values

Kategorie tematyczne

• 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1999
• Tom: 71
• Numer: 1
• Strony: 39-46

Daty

wydano

1999

otrzymano

1998-02-23

poprawiono

1998-10-14

Twórcy

autor

Jolanta Przybycin

• Department of Applied Mathematics, University of Mining and Metallurgy, Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

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• [2] R. Chiappinelli, On eigenvalues and bifurcation for nonlinear Sturm-Liouville operators, Boll. Un. Mat. Ital. A (6) 4 (1985), 77-83.
• [3] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
• [4] L. Nirenberg, Topics in Nonlinear Functional Analysis, New York Univ. Lecture Notes, 1973-74.
• [5] J. Przybycin, Nonlinear eigenvalue problems for fourth order ordinary differential equations, Ann. Polon. Math. 60 (1995), 249-253.
• [6] P. H. Rabinowitz, On bifurcation from infinity, J. Differential Equations 14 (1973), 462-475.
• [7] K. Schmitt and H. L. Smith, On eigenvalue problems for nondifferentiable mappings, J. Differential Equations 33 (1979), 294-319.