Abstract
Goodman proved that the pointwise infimum of all superfunctions is the minimal absolutely continuous solution of x′ = f (t, x), t ∈ [0, 1], x(0) = 0, in case f is a L1 -bounded Caratheodory function. How far can Caratheodory conditions be weakened without loosing that property? First we establish necessary conditions over f for Goodman’s method to be valid, and then we use them as a starting point to deduce sufficient ones. In this way we obtain new existence results and we provide new insights concerning the application of Goodman’s method. Mathematics subject classification (2000): 34A12, 34A36, 34A40.
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