This is an overview of the solvability of semilinear equations where the linear part has discrete spectrum. Semilinear elliptic and hyperbolic equations, as well as Hammerstein integral equations, are used as motivating examples. The presentation is intended to be accessible to non experts.
© 2004 American Mathematical Society
Castro, Alfonso. “Semilinear equations with discrete spectrum”, Contemporary Mathematics, 357 (2004), pp. 1-16.