Asymptotic behaviour of equations and
Asymptotic behaviour of the equation with complex-valued coefficients
Asymptotic behaviour of the system of two differential equations
Asymptotic estimates for the growth of meromorphic solutions to differential equations in angular domains.
Asymptotic expansions of solutions to the fifth Painlevé equation in neighbourhoods of singular and nonsingular points of the equation
Applying methods of plane Power Geometry we are looking for the asymptotic expansions of solutions to the fifth Painlevé equation in the neighbourhood of its singular and nonsingular points.
Asymptotic nature of solutions of the equation with a complex valued function
Asymptotics of polynomial solutions of a class of generalized Lamé differential equations.
Asymptotische Eigenschaften der Differentialgleichung
Asymptotische Formeln für die Lösungnen der Differentialgleichung
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...
Bäcklund transformations for first and second Painlevé hierarchies.
Bernstein classes
One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions....
Bernstein polynomials and spectral numbers for linear free divisors
We discuss Bernstein polynomials of reductive linear free divisors. We define suitable Brieskorn lattices for these non-isolated singularities, and show the analogue of Malgrange’s result relating the roots of the Bernstein polynomial to the residue eigenvalues on the saturation of these Brieskorn lattices.
Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
In this paper we consider Bessel equations of the type , where A is an nn complex matrix and X(t) is an nm matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
Bessel's differential equation and its Hyers-Ulam stability.
Birational canonical transformations and classical solutions of the sixth Painlevé equation
Bounded index, entire solutions of ordinary differential equations and summability methods.
Boutroux's method vs. re-scaling. Lower estimates for the orders of growth of the second and fourth Painlevé transcendents.
-conjugacy of holomorphic flows near a singularity