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

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  • Dorota Bors

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.

Suggested Citation

  • Dorota Bors, 2013. "Global Solvability of Hammerstein Equations with Applications to BVP Involving Fractional Laplacian," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:240863
    DOI: 10.1155/2013/240863
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    References listed on IDEAS

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    1. M. A. El-Ameen & M. El-Kady, 2012. "A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, April.
    2. M. A. El-Ameen & M. El-Kady, 2012. "A New Direct Method for Solving Nonlinear Volterra‐Fredholm‐Hammerstein Integral Equations via Optimal Control Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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