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Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball

Author

Listed:
  • Valery Karachik

    (Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia)

  • Batirkhan Turmetov

    (Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan)

  • Hongfen Yuan

    (School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China)

Abstract

Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann boundary value problems are studied. For the problems under consideration, existence and uniqueness theorems are proved. Necessary and sufficient conditions for the solvability of all problems are obtained and an integral representations of solutions are given in terms of the corresponding Green’s functions.

Suggested Citation

  • Valery Karachik & Batirkhan Turmetov & Hongfen Yuan, 2022. "Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 10(7), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1158-:d:786355
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    References listed on IDEAS

    as
    1. Valery Karachik, 2021. "Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    2. Cabada, Alberto & Tojo, F.Adrián F., 2017. "On linear differential equations and systems with reflection," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 84-102.
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    Cited by:

    1. Hongfen Yuan & Valery Karachik, 2023. "Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations," Mathematics, MDPI, vol. 11(9), pages 1-15, May.
    2. Valery Karachik, 2023. "Riquier–Neumann Problem for the Polyharmonic Equation in a Ball," Mathematics, MDPI, vol. 11(4), pages 1-21, February.

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