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On the Variational Method for the Existence of Solutions of Nonlinear Equations of Hammerstein Type

In: Djairo G. de Figueiredo - Selected Papers

Author

Listed:
  • Djairo G. de Figueiredo

    (University of Illinois, Department of Mathematics)

  • Chaitan P. Gupta

    (University of Brasilia, Department of Mathematics
    Northern Illinois University, Department of Mathematics)

Abstract

ABSTRACT Let X be a real Banach space and X* its conjugate Banach space. Let A be an unbounded monotone linear mapping from X to X* and N a potential mapping from X* to X. In this paper we establish the existence of a solution of the equation u + ANu = v for a given v in X* using variational method. Our method consists in using a splitting of A via an auxiliary Hilbert space and solving an equivalent equation in this auxiliary Hilbert space. In §2, we prove the same result in the case when X is a Hilbert space using the natural splitting of A in terms of its square root. We do this to compare and contrast the proofs in the two cases.

Suggested Citation

  • Djairo G. de Figueiredo & Chaitan P. Gupta, 1973. "On the Variational Method for the Existence of Solutions of Nonlinear Equations of Hammerstein Type," Springer Books, in: David G. Costa (ed.), Djairo G. de Figueiredo - Selected Papers, edition 127, pages 35-41, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02856-9_5
    DOI: 10.1007/978-3-319-02856-9_5
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