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Boundary Value Problem for an Odd Order Equation with Multiple Characteristics

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We prove the unique solvability of the nonlinear boundary value problem for an odd order nonlinear equation with multiple characteristics in a curvilinear domain. The uniqueness of a solution is established by the method of energy integrals by using some elementary inequalities and Friedrichs type inequalities. To prove the existence of a solution to this problem, an auxiliary problem is considered whose Green function is constructed. With the help of this auxiliary problem, the original problem is reduced to a system of Hammerstein integral equations. The solvability of the nonlinear system is proved by the contraction mapping principle.

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Authors and Affiliations

  1. Tashkent State University of Economics, 49, Islom Karimov St, Tashkent, Uzbekistan, 100066

    Odilzhan Kurbanov

  2. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, 9, University St, Tashkent, Uzbekistan, 100174

    Sirojiddin Z. Dzhamalov

  3. Central Asian University, 264, Milliy bog St, Tashkent, Uzbekistan, 111221

    Sirojiddin Z. Dzhamalov

  4. Yugra State University, 16, Chekhova St, Khanty-Mansiysk, 628012, Russia

    Sergey Pyatkov

  5. Academy of Sciences of the Republic of Sakha (Yakutia), 33, Lenin Av, Yakutsk, 677007, Russia

    Sergey Pyatkov

Authors
  1. Odilzhan Kurbanov
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  2. Sirojiddin Z. Dzhamalov
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  3. Sergey Pyatkov
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Correspondence to Sergey Pyatkov.

Additional information

International Mathematical Schools. Vol. 3. Mathematical Schools in Uzbekistan. In Memory of M. S. Salakhitdinov

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Kurbanov, O., Dzhamalov, S.Z. & Pyatkov, S. Boundary Value Problem for an Odd Order Equation with Multiple Characteristics. J Math Sci 274, 241–254 (2023). https://doi.org/10.1007/s10958-023-06592-x

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  • DOI: https://doi.org/10.1007/s10958-023-06592-x

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