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

In this paper we establish an existence of solution theorem and an existence of bifurcation point theorem for Hammerstein integral equation whose kernel is supposed neither symmetric nor positive defined. To prove our result, we use the Tychonoff fixed point theorem. In particular, our bifurcation result is directly comparable with an analogous one recently established by F. Faraci. (C) 2004 Elsevier Inc. All rights reserved.