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

Anna Pudelko

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.

Keywords


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

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