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We use lower and upper solutions to investigate the existence of the greatestand the least solutions for quasimonotone systems of measure differentialequations. The established results are then used to study the solvability ofStieltjes differential equations; a recent unification of discrete, continuousand impulsive systems. The applicability of our results is illustrated in asimple model for bacteria population.

Extremal solutions of systems of measure differential equations and applications in the study of Stieltjes differential problems