General Linear Boundary Value Problem for the Second-Order Integro-Differential Loaded Equation with Boundary Conditions Containing Both Nonlocal and Global Terms

and Applied Analysis 3 equation. Therefore, we will choose fundamental solution of the principal part of equation 2.1 , that is, for two-dimensional Laplace equation as follows: U x − ξ 1 2π ln|x − ξ|. 3.1 4. Basic Relations At first, we construct Green’s second formula connected with 2.1 and fundamental solution 3.1 , that is, we multiply 2.1 by fundamental solution 3.1 and integrate it with respect to domain D. Further, applying Ostrogradskii-Gauss formula, we get the following: ∫ Γ [ u x dU x − ξ dνx − du x dν U x − ξ ] dx − 2 ∑