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This paper proposes an approach for determining solutions sets of larger scale non linear equations systems with more unknowns number than equations. The proposed approach consists in transforming the equations system into a one dimensional equation by using α-dense curves properties. Then conditions for obtaining sets that are dense in the set of solution is established. An example is provided to demonstrate merits of our proposed algorithm. AMS Subject Classification: 34A35, 35F50, 57Q55

ON THE DETERMINATION OF SOLUTIONS SETS REGARDING HIGHLY NON-LINEAR EQUATIONS SYSTEMS