One-dimensionality of the kernel of the system of Fredholm integral equations for a homogeneous biharmonic problem

Abstract

A condition (doing a generalization of [Theorem 7.11, Gryshchuk S. V., Plaksa S. A. Monogenic functions in the biharmonic boundary value problem // Math. Meth. Appl. Sci. 2016. 39(11): 2939 – 2952]) under which a dimension of the linear space of solutions for a system of the Fredholm integral equations (associated with the homogeneous biharmonic boundary value problem) equals one is found.