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On the Index of Solvability for Variational Inequalities in Banach Spaces

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Abstract

We define the index of solvability, a topological characteristic, whose difference from zero provides the existence of a solution for variational inequalities of Stampacchia’s type with S +-type and pseudo-monotone multimaps on reflexive separable Banach spaces. Some applications to a minimization problem and to a problem of economical dynamics are presented.

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Authors and Affiliations

  1. Dipartimento di Energetica “S. Stecco”, Università di Firenze, Via S.Marta 3, 50139, Florence, Italy

    Irene Benedetti

  2. Faculty of Mathematics, Voronezh State University, Universitetskaya pl.,1, 394 006, Voronezh, Russia

    Valeri Obukhovskii

Authors
  1. Irene Benedetti
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  2. Valeri Obukhovskii
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Corresponding author

Correspondence to Irene Benedetti.

Additional information

The work is supported by the Russian FBR Grants 05-01-00100 and 07-01-00137 and by the NATO Grant ICS.NR.CLG 981757.

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Benedetti, I., Obukhovskii, V. On the Index of Solvability for Variational Inequalities in Banach Spaces. Set-Valued Anal 16, 67–92 (2008). https://doi.org/10.1007/s11228-007-0046-8

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