Func[b_, v_] :=
  NDSolve[{D[u[p], {p, 2}] + u[p] == 1/(2* (b*v) ^ 2) + 3/2* u[p]^ 2,
    u[0] == 0, u'[0] == 0}, {u[p]}, {p, 0, 28}];


U[p_, b_, v_] := u[p] /. First[Func[b, v]];

Rmin[bInit_, vInit_] :=
 MinValue[{(1/U[p, bInit, vInit]), 1 > p > 0}, p]

NSolve[1/U[p, 100, 0.01] == 1, p]