AbstractThe bifurcation of a solution of the equationf(x, λ) = 0 at the point (x0, λ0) is investigated. In the case thatB: = –fx(x0, λ0) is a FREDHOLM operator by the method of LJAPUNOV/SCHMIDT the original equation is equivalent to a system consisting of a locally uniquely solvable equation and an equation in a finit dimensional subspace, the so‐called bifurcation equation. For analytical/recursion formulas are deduced to determine the locally unique solution. In the case of FREDHOLM operatorsBwith index zero practicable criteria are given for the applicability of a theorem of IZE being a generalization of a well known theorem of KRASNOS
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