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Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type

Zabawa T.S.

Opuscula Mathematica

2006

Vol. 26, no. 1

173-183

A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as t → ∞ is the solution of the associated elliptic problem. The result is based on the monotone methods.

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

Zabawa T.S.

Opuscula Mathematica

2005

Vol. 25, no. 2

333-343

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 uper functions.