On projective equivalence of univariate polynomial subspaces.
On proper oscillatory and vanishing-at-infinity solutions of differential equations with a deviating argument.
On proper oscillatory solutions of the nonlinear differential equations of the -th order
On properties of derivatives of the basic central dispersion in an oscillatory equation with an almost periodic coefficient
On properties of nonlinear second-order systems under nonlinear impulse perturbations.
On properties of oscillatory solutions of non-linear differential equations of the n-th order
On properties of spectral approximations
On property (B) of higher order delay differential equations
In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the -th order delay differential equations Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases and are discussed.
On -summation and confluence
This paper is divided in two parts. In the first part we study a convergent -analog of the divergent Euler series, with , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding -difference equation. In the second part, we work under the assumption . In this case, at least four different -Borel sums of a divergent power series solution of an irregular singular...
On q-asymptotics for q-difference-differential equations with Fuchsian and irregular singularities
This work is devoted to the study of a Cauchy problem for a certain family of q-difference-differential equations having Fuchsian and irregular singularities. For given formal initial conditions, we first prove the existence of a unique formal power series X̂(t,z) solving the problem. Under appropriate conditions, q-Borel and q-Laplace techniques (firstly developed by J.-P. Ramis and C. Zhang) help us in order to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion...
On quadratically integrable solutions of the second order linear equation
Integral criteria are established for and , where is the space of solutions of the equation satisfying the condition
On Quasilinear Parabolic Systems.
On quasimonotone increasing systems of ordinary differential equations.
On quasiparabolical differential equations of higher order
On random boundary value problems for ordinary differential equations
On rational and periodic solutions of stationary KdV equations.
On rectifiable oscillation of Euler type second order linear differential equations.
On reducibility of linear quasiperiodic systems with bounded solutions.
On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits
We study conditions involving the critical set of a regular polynomial endomorphism f∶ℂ2↦ℂ2 under which all complete external rays from infinity for f have well defined endpoints.
On regularity of solutions to some problems of mathematical physics