Opuscula Math. 30, no. 1 (2010), 69-77
On some properties of the superposition operator on topological manifolds
Abstract. In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
Keywords: superposition operator, continuous function, topological manifold, Hammerstein integral equation.
Mathematics Subject Classification: 47H30, 45G15.
- Received: 2009-08-18.
- Revised: 2009-10-17.
- Accepted: 2010-10-23.