On the number of fixed points of nonlinear operators and applications. (English) Zbl 1131.47308

Summary: In this paper, the famous Amann three-solution theorem is generalized. The multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to a nonlinear system of Hammerstein integral equations.


47H10 Fixed-point theorems
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiń≠, Uryson, etc.)
47J05 Equations involving nonlinear operators (general)
47N20 Applications of operator theory to differential and integral equations