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Abstract and Applied Analysis
Volume 2013, Article ID 240863, 10 pages
Research Article

Global Solvability of Hammerstein Equations with Applications to BVP Involving Fractional Laplacian

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Received 19 July 2013; Accepted 6 November 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 Dorota Bors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some sufficient conditions for the nonlinear integral operator of the Hammerstein type to be a diffeomorphism defined on a certain Sobolev space are formulated. The main result assures the invertibility of the Hammerstein operator and in consequence the global solvability of the nonlinear Hammerstein equations. The applications of the result to nonlinear Dirichlet BVP involving the fractional Laplacian and to some specific Hammerstein equation are presented.