  We construct the type IIB supergravity solutions describing D3-branes ending
on 5-branes, in the near-horizon limit of the D3-branes. Our solutions are
holographically dual to the 4d N=4 SU(N) super-Yang-Mills (SYM) theory on a
half-line, at large N and large 't Hooft coupling, with various boundary
conditions that preserve half of the supersymmetry. The solutions are limiting
cases of the general solutions with the same symmetries constructed in 2007 by
D'Hoker, Estes and Gutperle. The classification of our solutions matches
exactly with the general classification of boundary conditions for D3-branes
ending on 5-branes by Gaiotto and Witten. We use the gravity duals to compute
the one-point functions of some chiral operators in the N=4 SYM theory on a
half-line at strong coupling, and find that they do not match with the
expectation values of the same operators with the same boundary conditions at
small 't Hooft coupling. Our solutions may also be interpreted as the gravity
duals of 4d N=4 SYM on AdS_4, with various boundary conditions.
