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A variational method is presented for directly finding the bifurcation pointof nonlinear equations as the saddle-node point of the extended nonlinearRayleigh quotient. The method is applied for solving an open problem on theexistence of a maximal saddle-node bifurcation point for set of positivesolutions of system equations with convex-concave type nonlinearity.

A finding of the maximal saddle-node bifurcation for systems of differential equations