Quasi-solutions, vector Lyapunov functions, and monotone method

The notion of quasi-solution which was introduced earlier has been developed in this paper. Further, the notion of coupled quasi-solutions and coupled maximal and minimal solutions has been introduced. It is shown that the idea of quasi-solutions leads to isolated subsystems, and has obtained error estimates between solutions and quasi-solutions. Also, monotone iterative techniques have been developed to obtain coupled maximal and minimal quasi-solutions.