Abstract and Applied Analysis

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

Dorota Bors

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 240863, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450377

Digital Object Identifier
doi:10.1155/2013/240863

Mathematical Reviews number (MathSciNet)
MR3139484

Zentralblatt MATH identifier
1291.45006

Citation

Bors, Dorota. Global Solvability of Hammerstein Equations with Applications to BVP Involving Fractional Laplacian. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 240863, 10 pages. doi:10.1155/2013/240863. https://projecteuclid.org/euclid.aaa/1393450377


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