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Selection of critical solutions in non-monotone vanishing discount problems
We study a generalized vanishing discount problem for Hamilton--Jacobi equations without assuming monotonicity either pointwise or in the averaged sense with respect to all Mather measures. Specifically, we consider \[ λa(x)u(x)+H\big(x,Du(x)\big)=c_0, \] and assume that, for every sufficiently smal
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