Spectral characteristics of a nonlocal problem for two linear systems of partial differential equations

Abstract

We study the boundary-value problem for a linear system of differential equations written in the form of differential-operator equations $$ aD_t u(t)+bBu(t)=f(t) $$ with nonlocal boundary conditions at $t$. Such a boundary value problem for a linear system of differential equations (including partial derivatives), we shall call nonlocal. The purpose of the article is to study the spectral characteristics of differential operators generated by the nonlocal task for the two linear systems of differential equations considered in a bounded region of finite-dimensional Euclidean space.

Keywords

• boundary value problem
• nonlocal conditions
• operator spectrum
• elliptic systems
• systems of differential equations
• riesz basis