In this note some well-known existence and multiplicity results of nontrivial solutions for scalar Hammerstein equations ,  are extended to equations in Hilbert spaces. The tools are a mountain pass theorem on closed convex substes of a Hilbert space due to Guo-Sun-Qi  and a new technique of checking the Palais-Smale compactness condition which was first presented in . The results compplement those established in .
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Hammerstein integral equation; compactness; critical point theory.
R. Precup, Nontrivial solvability of Hammerstein integral equations in Hilbert spaces, Seminaire de la Theorie de la Mielleure Approximation Convexite et Optimisation, Cluj-Napoca, 26 octombre – 29 octobre, 2000, pp. 255-265.
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Seminaire de la Theorie de la Meilleure Approximation, Convexite et Optimisation
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