Periodic solutions of nonlinear finite difference systems with time delays
Authors :
S.B. Kiwnea,*
Author Address :
aDepartment of Mathematics, Deogiri College, Aurangabad–431005, Maharashtra, India.
*Corresponding author.
Abstract :
In this paper a coupled system of nonlinear finite difference equations corresponding to a class of periodicparabolic systems with time delays and with nonlinear boundary conditions in a bounded domain is investigated. Using the method of upper-lower solutions two monotone sequences for the finite di.erence system are constructed. Existence of maximal and minimal periodic solutions of coupled system of finite di.erence equations with nonlinear boundary conditions is also discussed. The proof of existence theorem is based on the method of upper-lower solutions and its associated monotone iterations. It is shown that the sequence of iterations converges monotonically to unique solution of the nonlinear finite di.erence system with time delays under consideration.
Keywords :
Periodic solution, periodic parabolic system, finite difference equation, upper and lower solution, quasimonotone nondecreasing function.
DOI :
Article Info :
Received : November 11, 2012; Accepted : July 10, 2013.
