Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball
Karachik V. Turmetov B. Yuan H.
April-1 2022MDPI
Mathematics
2022#10Issue 7
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.
biharmonic equation , Dirichlet problem , existence and uniqueness , Green’s function , Navier problem , Neumann problem , nonlocal equation , Riquier–Neumann problem
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Department of Mathematical Analysis, South Ural State University (NRU), Chelyabinsk, 454080, Russian Federation
Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, 161200, Kazakhstan
School of Mathematics and Physics, Hebei University of Engineering, Handan, 056038, China
Department of Mathematical Analysis
Department of Mathematics
School of Mathematics and Physics
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