Sharp estimates for the Ambrosetti-Hess problem and consequences

Motivated by {3}, we define the "Ambrosetti-Hess problem" to be the problem of bifurcation from infinity and study of the local behavior of continua of solutions of nonlinear elliptic eigenvalue problems. Although the works in this way underline the asymptotic properties on the nonlinearity, here we point out that this local behavior is determined by the global shape of the nonlinearity.