Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
Volume 72 / 1999
Annales Polonici Mathematici 72 (1999), 15-24 DOI: 10.4064/ap-72-1-15-24
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.