@unpublished{ShlapunovTarkhanov2007,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Formal Poincar{\´e} lemma},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30231},
  year      = {2007},
  abstract  = {We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.},
  language  = {en}
}
@unpublished{ChenLi2007,
  author    = {Chen, Hua and Li, Ke},
  title     = {The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30247},
  year      = {2007},
  abstract  = {Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.},
  language  = {en}
}
@unpublished{YagdjianGalstian2007,
  author    = {Yagdjian, Karen and Galstian, Anahit},
  title     = {Fundamental solutions for wave equation in de Sitter model of universe},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30271},
  year      = {2007},
  abstract  = {In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp - Lq-decay estimates for the solutions of the equation with and without a source term.},
  language  = {en}
}
@unpublished{ChenLiXu2007,
  author    = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang},
  title     = {Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30283},
  year      = {2007},
  abstract  = {This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.},
  language  = {en}
}
@unpublished{LyTarkhanov2007,
  author    = {Ly, I. and Tarkhanov, Nikolai Nikolaevich},
  title     = {The cauchy problem for nonlinear elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30228},
  year      = {2007},
  abstract  = {This paper is devoted to investigation of the Cauchy problem for nonlinear elliptic equations with a small parameter.},
  language  = {en}
}
@unpublished{YinHua2007,
  author    = {Yin, Yang and Hua, Chen},
  title     = {On chemotaxis systems with saturation growth},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30254},
  year      = {2007},
  abstract  = {In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.},
  language  = {en}
}
@unpublished{FladSchneiderSchulze2007,
  author    = {Flad, Heinz-J{\"u}rgen and Schneider, Reinhold and Schulze, Bert-Wolfgang},
  title     = {Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30268},
  year      = {2007},
  abstract  = {We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.},
  language  = {en}
}