Auszug aus einem Schreiben des Herrn L. Fuchs an C. W. Borchardt.
Automorphic realization of residual Galois representations
We show that it is possible in rather general situations to obtain a finite-dimensional modular representation of the Galois group of a number field as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...
Averaging for ordinary differential equations perturbed by a small parameter
In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity in...
Averaging in an ordinary differential equation.
Averaging method for differential equations perturbed by dynamical systems
In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...
Averaging method for differential equations perturbed by dynamical systems
In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...
Averaging method for neutral type impulsive differential equations with supremums
Averaging of multivalued differential equations.
Averaging results for functional-differential equations.
Averaging technique and oscillation for even order damped delay differential equations.
Averaging techniques and oscillation of quasilinear elliptic equations
By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.