Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel (Q1888230)

This paper deals with an existence theorem of solutions and of bifurcation points for the Hammerstein integral equation \[ u(x)=\lambda\int_{\Omega}k(x,y)f(y,u(y))dy, \] where \(\lambda\in \mathbb R\), \(\Omega\) is a Lebesgue measurable subset of \(\mathbb R^{n}, \;k\in L^{\infty}(\Omega\times\Omega)\) and \(f:\Omega\times \mathbb R\to \mathbb R\) is a Carathéodory function. The proofs rely on the Tychonoff fixed point theorem.