Abstract

Resolving Systems Reduction Possibilities in Stationary Bifurcation Theory

I.V.Konopleva, B.V.Loginov (Department of Higher Mathematics, Ulyanovsk State Technical University, Ulyanovsk, Russia)

e-mail: loginov@ulstu.ru

In Banach spaces it is considered nonlinear equation with complex bifurcational parameter and densely defined closed linear Fredholm operators, the nonlinear term is sufficiently smooth. Beginning with the first works (V.I.Yudovich (1967), B.V. Loginov and V.A. Trenogin (1971)) on the usage of group symmetry conditions for nonlinear equation the question about simultaneous reduction of branching equation (BEq) on unknowns and equations (truncation reduction) has remained open. Here it is solved for the more general finitedimensional equivalent of nonlinear equation - BEq in the root subspace (BEqR). As corollary we obtain the corresponding results for Beq. The results and designations of our communications on the Kasnoyarsk international Conference "Symmetry and differential equations"-2000 and previous MOGRAN-VIII are used.

Section : 12