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Abstrakty
In this paper we discuss the bifurcation problem for the abstract operator equation of the form F(u,λ)=θ with a parameter lambda, where F:X x R -> Y is a C^1 mapping, X, Y are Banach spaces. By the bounded linear generalized inverse A^+ of A=F_u(u_0 λ_0), an abstract bifurcation theorem for the case dim N(F_u(u_0 λ_0)) >= codim R(F_u(u_0,λ_0))=1 has been obtained
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
145--150
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Departament of Mathematics, Northeast Normal University, China
autor
- Departament of Mathematics, Northeast Normal University, China
Bibliografia
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- [2] M. G. Crandall and P. H. Rabinowicz, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Ration Mech. Anal. 52 (1973), 161-180.
- [3] J. P. Shi, Persistence and bifurcation of degenerate solution, J. Functional Analysis 168(2) (1990), 494-531.
- [4] X. C. He and W. Y. Sun, The generalized inverse for matrices, Jiangsu Science Press 1990.
- [5] C. K. Zhong, X. L. Fan and W. Y. Chen, Introduction to Nonlinear Functional Analysis, Lanzhou University Press 1998 (in Chinese).
- [6] X. M. Sun, H. C. Yin and Y. W. Wang, The generalized Lyapunov-Schmidt Process in the Bifurcation Theory of Nonliear Operator Eqation, Mathmatics In Practice and Theory 33(5) (2003), 108-114 (in Chinese).
- [7] M. S. Berger, Nonlinearity and functional analysis, Academic Press New York 1977.
- [8] K. Deimling, Nonlinear functional analysis, Springer Verlag Berlin 1985.
- [9] M. Golubisky, D. G. Schaeffer, Singularities and groups in bifurcation theory, Vol I, Springer Verlag Berlin 1985.
- [10] T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problem, J. Diff. Eq. 146(1) (1998), 121-156.
- [11] J. Shi, Persistence and Bifurcation of Degenerate Solutions, J. Func. Anal. 169(2) (1999), 494-531.
- [12] Y. W. Wang and H. Wang, Generalized orthogonal decomposion theorem in Banach space and generalized orthogonal complemented subspace, Acta Math. Sinica 44(6) (2001), 1045-1050 (in Chinese).
- [13] M. Z. Nashed, Ed. Generalized Inverse and Applications, Academic Press, New York-London 1976.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0008-0051