Opuscula Math. 25, no. 2 (2005), 333-343
Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
Tomasz S. Zabawa
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.
Mathematics Subject Classification: 35J45, 35J65, 35R10, 47H07.