Second order differentiability and Lipschitz smooth points of convex functionals
Semi-continuity and weak-continuity
Semi-contractions des espaces localement compacts et cas des variétés complexes
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.
Semireflexive Spaces In Which The Theorem On The Derivative-Of-The-Inverse Fails For Frechet Derivatives.
Separable solutions of quasilinear Lane–Emden equations
For and either or , we prove the existence of solutions of in a cone , with vertex 0 and opening , vanishing on , of the form . The problem reduces to a quasilinear elliptic equation on 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.
Sharp bounds for the intersection of nodal lines with certain curves
Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between and is . This bound is sharp.
Simple singularities of functions on supermanifolds.
Singlevaluedness of monotone operators on subspaces of GSG spaces
We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a -cone supported set.
Singular Hamiltonian systems and symplectic capacities
The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless...
Singuläre Integrale mit gemsichten Homogenitäten auf Mannigfaltigkeiten und Anwendungen in der Funktionentheorie.
Singularités de bord : dualité, formules de Picard Lefschetz relatives et diagrammes de Dynkin
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Singularities of envelopes of families of submanifolds in
Singularities of implicit differential systems and maximum principle
The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding...
Singularities of implicit differential systems and their integrability
Singularities of k-tuples of vector fields [Book]
Singularities of the maximum function over a preimage
Singularities of Vector Fields on the Plane With Pointed Direction.
Slices for Proper Actions of non-Compact lie groups
Small time-periodic solutions to a nonlinear equation of a vibrating string
In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.