The main idea of the project: research of new classes of differential and functional-differential equations, inequalities and systems and the application of the obtained results to interdisciplinary research in mathematical models of physical and biological processes.

The project analyzes boundary value problems for elliptic functional-differential equations in bounded domains and half-space, as well as elliptic functional-differential equations in the entire space R^n.

To study linear elliptic differential-difference equations, symmetrized matrices corresponding to difference operators are used, while the skew-symmetric component does not violate the strong ellipticity of the linear operator and the smoothness properties of generalized solutions. Previously, the solvability criteria for nonlinear elliptic differential-difference equations were proposed, in which the difference operators are described by symmetric matrices. It was shown that, unlike the linear case for nonlinear problems, the skew-symmetric part affects ellipticity. In this project, we propose to use previously developed methods to study nonlinear elliptic problems with difference operators, which correspond to triangular matrices.