Nontrivial Solutions of Abstract Hammerstein Equations

Abstract

This chapter deals with nontrivial solvability in balls of abstract Hammer-stein equations and Hammerstein integral equations in R ⁿ by a variational approach. The variational method for treating Hammerstein integral equations goes back to the papers of Hammerstein [17] and Golomb [15]. For further contributions see the monographs by Krasnoselskii [19], Krasnoselskii-Zabreiko-Pustylnik-Sobolevskii [20] and Vainberg [43]. For more recent results see the papers by Moroz-Vignoli-Zabreiko [24] and Moroz-Zabreiko [25], [26]. The results presented in this chapter were adapted from Precup [31]–[34].