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Topological Methods in Nonlinear Analysis

Equilibria on $L$-retracts in Riemannian manifolds
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Equilibria on $L$-retracts in Riemannian manifolds

Authors

  • Seyedehsomayeh Hosseini
  • Mohamad R. Pouryayevali

DOI:

https://doi.org/10.12775/TMNA.2016.017

Keywords

Set-valued map, degree theory, Euler characteristic, equilibrium

Abstract

We introduce a class of subsets of Riemannian manifolds called the $L$-retract. Next we consider a topological degree for set-valued upper semicontinuous maps defined on open sets of compact $L$-retracts in Riemannian manifolds. Then, we present a theorem on the existence of equilibria (or zeros) of an upper semicontinuous set-valued map with nonempty closed convex values satisfying the tangency condition defined on a compact $L$-retract in a Riemannian manifold.

References

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S. Hosseini and M.R. Pouryayevali, Euler characterization of epi-Lipschitz subsets of Riemannian manifolds, J. Convex. Anal. 20 (2013), 67–91.

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Published

2016-06-01

How to Cite

1.
HOSSEINI, Seyedehsomayeh and POURYAYEVALI, Mohamad R. Equilibria on $L$-retracts in Riemannian manifolds. Topological Methods in Nonlinear Analysis. Online. 1 June 2016. Vol. 47, no. 2, pp. 579 - 592. [Accessed 5 July 2025]. DOI 10.12775/TMNA.2016.017.
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