Galois properties of linear differential equations
Gauge-equivalent deformations of linear ordinary differential operators with constant coefficients.
Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
We associate to any convenient nondegenerate Laurent polynomial on the complex torus a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of (or its universal unfolding) and of the corresponding Hodge theory.
General solution of overdamped Josephson junction equation in the case of phase-lock.
Generalization of Okamoto's equation to arbitrary Schlesinger system.
Generalized trigonometric functions in complex domain
We study extension of -trigonometric functions and to complex domain. For , the function satisfies the initial value problem which is equivalent to (*) in . In our recent paper, Girg, Kotrla (2014), we showed that is a real analytic function for on , where . This allows us to extend to complex domain by its Maclaurin series convergent on the disc . The question is whether this extensions satisfies (*) in the sense of differential equations in complex domain. This interesting...
Generating operator of or Gaudin transfer matrices has quasi-exponential kernel.
Gevrey series of arithmetic type. I: Purity and duality theorems. (Séries Gevrey de type arithmétique. I: Théorèmes de pureté et de dualité.)
Gevrey series of arithmetic type. II: Transcendence without transcendence. (Séries Gevrey de type arithmétique. II: Transcendance sans transcendance.)
Global properties of the Painlevé transcendents: new results and open questions.
Groupe de Galois différentiel local et représentation adjointe
Dans cet article on s’intéresse à la représentation adjointe du tore exponentiel sur l’algèbre de Lie du groupe de Galois différentiel local. Nous proposons un algorithme pour réduire les sous-espaces poids de dimension supérieure à 1 à des sous-espaces de racines. Ce faisant, on construit un tore (en général) maximal qui contient le tore exponentiel. Au cours de ce travail on est amené à étudier la régularité du tore exponentiel dans le groupe de Galois local.
Growth and fixed points of meromorphic solutions of higher order linear differential equations
We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.
Growth and oscillation of differential polynomials in the unit disc.
Growth and oscillation of solutions to linear differential equations with entire coefficients having the same order.
Growth and oscillation of some class of differential polynomials in the unit disc
Growth and oscillation theory of solutions of some linear differential equations
Growth estimates for solutions of linear complex differential equations.
Growth of meromorphic solutions of higher-order linear differential equations.
Growth of solutions of a class of complex differential equations
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].
Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients.