Multiplicity results to nonlinear Hammerstein integral equations and applications (Q1980426)

Let \(I\) be a real interval, \(f\) and \(h\) be positive continuous functions on \(I\) satisfying certain assumptions and \(G\) be a function defined on \(I^2\). The purpose of the authors is to show that for \(t\in I\), the equation \[\displaystyle u(t)=\int_0^\omega G(t,s)h(s)f(u(s))ds\] has at least three solutions such that \(\omega=1\) if \(I=[0,1]\) and \(\omega=\infty\) if \(I=[0,\infty)\). The proof is based on the Leggett-Williams fixed point theorem.