  For the nonlocal Davey-Stewartson I equation, the Darboux transformation is
considered and explicit expressions of the solutions are obtained. Like the
nonlocal equations in 1+1 dimensions, many solutions may have singularities.
However, by suitable choice of parameters in the solutions of the Lax pair, it
is proved that the solutions obtained from seed solutions which are zero and an
exponential function of $t$ respectively, by a Darboux transformation of degree
$n$ are global solutions of the nonlocal Davey-Stewartson I equation. The
derived solutions are soliton solutions when the seed solution is zero, in the
sense that they are bounded and have $n$ peaks, and "line dark soliton"
solutions when the seed solution is an exponential function of $t$, in the
sense that they are bounded and their norms change fast along some straight
lines.
