Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type

Abstract

The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.

Keywords

• infinite systems
• elliptic differential-functional equations
• monotone iterative technique
• Chaplygin's method
• Dirichlet problem