On some properties of the superposition operator on topological manifolds

• Autorzy: Dronka J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

superposition operator; continuous function; topological manifold; Hammerstein integral equation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2010
• Tom: Vol. 30, no. 1
• Strony: 69--77
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Dronka J.

• Technical University of Rzeszów Department of Mathematics ul. W. Pola 2, 35-959 Rzeszów, Poland,

Bibliografia

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• [3] J. Dronka, L. Olszowy, The superposition operator for vector-valued functions on a noncompact interval, Demonstratio Math. 39 (2006), 411–418.
• [4] N. Dunford, J. Schwartz, Linear Operators I, Int. Publ., Leyden, 1963.
• [5] R. Engelking, General Topology, PWN Polish Scientific Publishers, Warsaw, 1977.
• [6] D. O’Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Acad. Publ., Dordrecht, 1998.
• [7] M.M. Postnikov, Lectures in Geometry. III. Smooth Manifolds, Mir Publishers, Moscow, 1989.
• [8] P.P. Zabrejko, A.I. Koshelev, M.A. Krasnosel’skii, S.G. Mikhlin, L.S. Rakovschik, V.J. Stecsenko, Integral Equations, Nordhoff, Leyden, 1975.