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

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.

Keywords

• nonlocal equation
• biharmonic equation
• Dirichlet problem
• Neumann problem
• Navier problem
• Riquier–Neumann problem