A remark on real parameter global bifurcation (Q1272193)

The paper treats the nonlinear eigenvalue problem \(F(x,\lambda) = L(\lambda)x + R(x,\lambda)=0\), where \(F: X\times {\mathbb{R}} \mapsto X\) with \(X\) a Hilbert space. If \(L(\lambda)\) is a polynomial in \(\lambda\), then it is shown that under some easily verifiable conditions \(\lambda_0 > 0\) is a global bifurcation point. The proof relies heavily on Brouwer topological degree techniques and a previous result by the author. Finally the theorem is applied to a simple ordinary differential equation.