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- W339155821 abstract "Publisher Summary This chapter discusses multiple eigenvalue bifurcation for holomorphic mappings. The existence of nontrivial solutions of the equation λu-Lu -V(u) = θ is studied in H x R , where H is a real Hilbert space; L is a bounded, compact, and symmetric linear operator acting in H; and V is a nonlinear operator, which is holomorphic in a neighborhood of θ . Thus, V has, locally, a representation as a series of continuous homogeneous operators. It is assumed that in this representation, the homogeneous operator of the lowest order V k , k> 1, is the strong gradient of a C 1 -functional l. l is not assumed to be weakly continuous. The holomorphy suggests satisfactory results for a complex space. Bifurcation has been proved with weak non-degeneracy assumptions for complex solutions. The chapter also defines the total eigenprojections corresponding to the group of eigenvalues that emanate from 0 when v is chosen in a neighborhood of the origin." @default.
- W339155821 created "2016-06-24" @default.
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- W339155821 date "1971-01-01" @default.
- W339155821 modified "2023-09-27" @default.
- W339155821 title "Multiple Eigenvalue Bifurcation for Holomorphic Mappings" @default.
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- W339155821 doi "https://doi.org/10.1016/b978-0-12-775850-3.50008-x" @default.
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