Sobolev periodic solutions of a partial differential equation with coefficients which depend on a parameter

  • V.S. Il'kiv Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine
  • I.Ya. Savka Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • M.M. Symotyuk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
Keywords: differential equation, periodic solution, small denominator, diophantine approximation, metric estimation
Published online: 2013-12-30

Abstract


The conditions of existence and uniqueness of Sobolev periodic solution for linear partial differential equation with constant complex coefficients, which depends on one real parameter, are established. It is shown that these conditions fulfill for almost all (with respect to the Lebesgue measure) parameter values.
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How to Cite
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Il’kivV., SavkaI., SymotyukM. Sobolev Periodic Solutions of a Partial Differential Equation With Coefficients Which Depend on a Parameter. Carpathian Math. Publ. 2013, 5 (2), 249-255.

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