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June 2004 Bifurcation of Nonlinear Equations: I. Steady State Bifurcation
Tian Ma, Shouhong Wang
Methods Appl. Anal. 11(2): 155-178 (June 2004).

Abstract

We prove in this article some general steady state bifurcation theorem for a class of nonlinear eigenvalue problems, in the case where algebraic multiplicity of the eigenvalues of the linearized problem is even. These theorems provide an addition to the classical Krasnoselskii and Rabinowitz bifurcation theorems, which require the algebraic multiplicity of the eigenvalues is odd. For this purpose, we prove a spectral theorem for completely continuous fields, which can be considered as a generalized version of the classical Jordan matrix theorem and the Fredholm theorem for compact operators. An application to a system of second order elliptic equations is given as well.

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Tian Ma. Shouhong Wang. "Bifurcation of Nonlinear Equations: I. Steady State Bifurcation." Methods Appl. Anal. 11 (2) 155 - 178, June 2004.

Information

Published: June 2004
First available in Project Euclid: 17 June 2005

zbMATH: 1095.47027
MathSciNet: MR2143518

Rights: Copyright © 2004 International Press of Boston

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Vol.11 • No. 2 • June 2004
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