On a generalized Collatz-Wielandt formula and finding saddle-node bifurcations

Yavdat Il'yasov

We introduce the nonlinear generalized Collatz-Wielandt formula $${\lambda }^{\ast }=\underset{x\in Q}{\sup }\underset{i:h_i(x)\ne 0}{\min }\frac{g_i(x)}{h_i(x)},Q\subset {\mathbb{R}}^n,$$ and prove that its s…