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

Dorota Bors

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:240863

DOI: 10.1155/2013/240863

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