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Nielsen theory of transversal fixed point sets (with an appendix: C ∞ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovski (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.

Periodic segments and Nielsen numbers

Klaudiusz Wójcik (1999)

Banach Center Publications

We prove that the Poincaré map φ ( 0 , T ) has at least N ( h ˜ , c l ( W 0 W 0 - ) ) fixed points (whose trajectories are contained inside the segment W) where the homeomorphism h ˜ is given by the segment W.

Semi-contractions des espaces localement compacts et cas des variétés complexes

Jean-Jacques Loeb (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

En nous inspirant d’articles de Beardon, nous donnons des résultats concernant les points fixes et les orbites d’auto-applications contractantes et semi-contractantes des espaces connexes localement compacts. Des résultats plus précis sont obtenus dans le cas des variétés complexes Kobayashi hyperboliques.

Separable solutions of quasilinear Lane–Emden equations

Alessio Porretta, Laurent Véron (2013)

Journal of the European Mathematical Society

For 0 < p - 1 < q and either ϵ = 1 or ϵ = - 1 , we prove the existence of solutions of - Δ p u = ϵ u q in a cone C S , with vertex 0 and opening S , vanishing on ∂ C S , of the form u ( x ) = x - β ω ( x / x ) . The problem reduces to a quasilinear elliptic equation on S and the existence proof is based upon degree theory and homotopy methods. We also obtain a nonexistence result in some critical case by making use of an integral type identity.

Weakly coercive mappings sharing a value

J. M. Soriano (2011)

Czechoslovak Mathematical Journal

Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over 𝕂 has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method.

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