### Monotone iterative method for infinite systems of parabolic functional-differential equations with nonlocal initial conditions

#### Abstract

The nonlocal initial value problem for an infinite system

of parabolic semilinear functional-differential equations is studied.

General operators of parabolic type of second order with variable

coefficients are considered and the system is weakly coupled.

We prove a theorem on existence of a classical solution in the

class of continuous bounded functions and in the class of continuous

functions satisfying a certain growth condition. Partial uniqueness

result is obtained as well.

of parabolic semilinear functional-differential equations is studied.

General operators of parabolic type of second order with variable

coefficients are considered and the system is weakly coupled.

We prove a theorem on existence of a classical solution in the

class of continuous bounded functions and in the class of continuous

functions satisfying a certain growth condition. Partial uniqueness

result is obtained as well.

#### Keywords

Infinite systems; nonlocal parabolic Cauchy problem; functional-differential equations and inequalities; existence and uniqueness of solutions; monotone iterative method

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