## Topological Methods in Nonlinear Analysis

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

Anna Pudełko

#### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 36, Number 1 (2010), 101-117.

Dates
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.tmna/1461251066

Mathematical Reviews number (MathSciNet)
MR2744834

Zentralblatt MATH identifier
1220.35181

#### Citation

Pudełko, Anna. Monotone iterative method for infinite systems of parabolic functional-differential equations with nonlocal initial conditions. Topol. Methods Nonlinear Anal. 36 (2010), no. 1, 101--117. https://projecteuclid.org/euclid.tmna/1461251066

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