@article{AlsaedyTarkhanov2014,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  volume    = {95},
  journal   = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0362-546X},
  doi       = {10.1016/j.na.2013.09.024},
  pages     = {468 -- 482},
  year      = {2014},
  abstract  = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.},
  language  = {en}
}
@article{KiselevTarkhanov2014,
  author    = {Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich},
  title     = {The capture of a particle into resonance at potential hole with dissipative perturbation},
  series = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  volume    = {58},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2013.11.003},
  pages     = {27 -- 39},
  year      = {2014},
  abstract  = {We study the capture of a particle into resonance at a potential hole with dissipative perturbation and external periodic excitation. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.},
  language  = {en}
}
@article{BagderinaTarkhanov2014,
  author    = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Differential invariants of a class of Lagrangian systems with two degrees of freedom},
  series = {Journal of mathematical analysis and applications},
  volume    = {410},
  journal   = {Journal of mathematical analysis and applications},
  number    = {2},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-247X},
  doi       = {10.1016/j.jmaa.2013.08.015},
  pages     = {733 -- 749},
  year      = {2014},
  language  = {en}
}
@article{KiselevTarkhanov2014,
  author    = {Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {Scattering of trajectories at a separatrix under autoresonance},
  series = {Journal of mathematical physics},
  volume    = {55},
  journal   = {Journal of mathematical physics},
  number    = {6},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4875105},
  pages     = {24},
  year      = {2014},
  abstract  = {The subject of this paper is solutions of an autoresonance equation. We look for a connection between the parameters of the solution bounded as t -> -infinity, and the parameters of two two-parameter families of solutions as t -> infinity. One family consists of the solutions which are not captured into resonance, and another of those increasing solutions which are captured into resonance. In this way we describe the transition through the separatrix for equations with slowly varying parameters and get an estimate for parameters before the resonance of those solutions which may be captured into autoresonance. (C) 2014 AIP Publishing LLC.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2014,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {An index formula for Toeplitz operators},
  volume    = {3},
  number    = {12},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499},
  pages     = {24},
  year      = {2014},
  abstract  = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.},
  language  = {en}
}
@unpublished{MakhmudovTarkhanov2014,
  author    = {Makhmudov, Olimdjan and Tarkhanov, Nikolai Nikolaevich},
  title     = {The first mixed problem for the nonstationary Lam{\´e} system},
  volume    = {3},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71923},
  pages     = {19},
  year      = {2014},
  abstract  = {We find an adequate interpretation of the Lam{\´e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam{\´e} system.},
  language  = {en}
}
@unpublished{SultanovKalyakinTarkhanov2014,
  author    = {Sultanov, Oskar and Kalyakin, Leonid and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic perturbations of dynamical systems with a proper node},
  volume    = {3},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70460},
  pages     = {12},
  year      = {2014},
  abstract  = {The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.},
  language  = {en}
}
@unpublished{AizenbergTarkhanov2014,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {An integral formula for the number of lattice points in a domain},
  volume    = {3},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70453},
  pages     = {7},
  year      = {2014},
  abstract  = {Using the multidimensional logarithmic residue we show a simple formula for the difference between the number of integer points in a bounded domain of R^n and the volume of this domain. The difference proves to be the integral of an explicit differential form over the boundary of the domain.},
  language  = {en}
}
@unpublished{DyachenkoTarkhanov2014,
  author    = {Dyachenko, Evgueniya and Tarkhanov, Nikolai Nikolaevich},
  title     = {Singular perturbations of elliptic operators},
  volume    = {3},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69502},
  pages     = {21},
  year      = {2014},
  abstract  = {We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.},
  language  = {en}
}