Interlaced equations in branching theory. (Q1432509)

Let \(E_1\) and \(E_2\) be real Banach spaces and \(\Lambda\) be a real normed space. The problem of small solutions \(x(\lambda)\) construction for the equation \(F(x,\lambda)\equiv Bx-R(x,\lambda)=0\) is considered, where \(B:D\subset E_1\rightarrow E_2\) is a closed Noetherian operator with \(d\)-characteristic \((n,m)\). The authors generalize some of the reviewer's results (see, for example, the review article [\textit{B. V. Loginov}, Vestn. Samar. Gos. Univ., Mat. Mekh. Fiz. Khim. Biol. 1998, No. 4(10), 15--70 (1998; Zbl 1070.47523)]) concerning bifurcation theory under group symmetry conditions in the case of intertwined operators.