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Technical Report 124


In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for initial and boundary value problems of ordinary differential systems, it becomes necessary to impose a condition generally known as quasi-monotone property [1,3,5]. In systems which represent physical situations such as a model governing the combustion of a material, quasi-monotonicity is not satisfied, see [4]. However a kind of mixed monotone property holds. To deal with such situations the notion of quasi-solutions was systematically developed in [4]. In this paper, we investigate monotone iterative method for systems of nonlinear boundary value problems when the system possesses a mixed quasi-monotone property. This appears a natural setup for considering quasi-solutions and quasi-extremal solutions in view of the fact extremal solutions need not exist when quasi-monotone property does not hold. Furthermore, the results obtained include as special cases the known results corresponding to quasi-monotone property.


Mathematics | Physical Sciences and Mathematics

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