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Moment sequences and abstract Cauchy problems

Claus Müller (2003)

Commentationes Mathematicae Universitatis Carolinae

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.

Monodromy and topological classification of germs of holomorphic foliations

David Marín, Jean-François Mattei (2012)

Annales scientifiques de l'École Normale Supérieure

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.

Monotone convolution semigroups

Takahiro Hasebe (2010)

Studia Mathematica

We study how a property of a monotone convolution semigroup changes with respect to the time parameter. Especially we focus on "time-independent properties": in the classical case, there are many properties of convolution semigroups (or Lévy processes) which are determined at an instant, and moreover, such properties are often characterized by the drift term and Lévy measure. In this paper we exhibit such properties of monotone convolution semigroups; an example is the concentration of the support...

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang, Alberto Cabada, Juan J. Nieto (1993)

Annales Polonici Mathematici

The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

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