Consider the following code:

Clear["Global`*"]
            h[e_, u_] := (e + u) Log[
                 u/(e + u)] + (1 - e - u) Log[(1 - u)/(1 - e - u)];
            Y = 10000000;
            t = {0.10, 0.15, 0.16};
            a = 0.05;
            n = 56;
            NSolve[Exp[n*h[u - Total[t]/n, 1 - u]] == a/2 && 1 >= u >= 0, u]
            NSolve[Exp[n*h[u - Total[t]/n, 1 - u]] == a/2 && 1 >= u >= 0.01, u]

Hello The first one with NSolve works and gives that answer

{{u -> 3.34543*10^-7}, {u -> 0.0879319}}

But the second dosent

{}

What's is the problem with the second one if I want to get one root that satisfies 1 >= u >= 0.01?