We give an alternative view of the results published in the Herzog’s and Lemmert’s paper "On maximal and minimal solutions for \(x'(t) = F(t, x(t), x(h(t)))\), \(x(0) = x_0\)", Comment. Math. XL (2000), 93-102. One can observe that these results can be obtained by classical (elementary) methods, instead of Tarski’s fixed point theorems in partially ordered spaces.
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The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.
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