On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
On solvability of equations of the th order with jumping nonlinearities
On stable solutions of quasilinear periodic-parabolic problems
On the absence of Poincaré lemma for some systems of partial differential equations
On the asymptotic behavior of solutions of linear parabolic equations in space
On the asymptotics of solutions to the second initial boundary value problem for Schrödinger systems in domains with conical points
In this paper, for the second initial boundary value problem for Schrödinger systems, we obtain a performance of generalized solutions in a neighborhood of conical points on the boundary of the base of infinite cylinders. The main result are asymptotic formulas for generalized solutions in case the associated spectrum problem has more than one eigenvalue in the strip considered.
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the Cauchy problem for linear PDEs with retarded arguments at derivatives
We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.
On the complete integrability of an equation having solitons but not known to have a lax pair.
On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions
This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes...
On the derivation of the modified equation for the analysis of linear numerical methods
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the discretization of degenerate sweeping processes.
On the envelope of regularity for solutions of homogeneous systems of linear partial differential operators
On the existence and regularity of solutions of linear equations in spaces
On the existence of global holomorphic solutions of differential equations with complex parameters
On the Existence of Solutions of Certain Asymptotically Homogeneous Problems.
On the existence of solutions to a fourth-order quasilinear resonant problem.
On the global Cauchy problem for some non linear Schrödinger equations