Ambrosetti-Prodi type result of first-order differential equations with locally coercive nonlinearities (Q6072927)

The authors obtain an Ambrosetti-Prodi-type result for the \(T\)-periodic problem associated with the first-order differential equation \[ u'(t)=a(t)u(t)-f(t,u(t))+s. \] Here, \(a :{\mathbb R} \to [0, +\infty)\) is a \(T\)-periodic function with \(\int_0^T a(t)\,dt = 0\), the function \(f\) is of Carathéodory type, \(T\)-periodic with respect to its first variable, and satisfies some local coercivity at infinity, while \(s\) is a real parameter. The proof makes use of topological degree theory.