= Solution
The common <Neumann boundary conditions> define a $(p+1)$-dimensional timelike <worldvolume>: one time direction and $p$ spatial directions. The remaining <Dirichlet boundary conditions> fix its transverse position. An open string therefore ends on a <D-brane> of spatial dimension $p$, a D$p$-brane. For the critical <bosonic string theory> there are $25-p$ transverse directions.
If the Dirichlet constants agree at the two endpoints, both ends lie on the same planar <D-brane>. If they differ, the string stretches between two parallel <D-branes> with the same orientation but different positions. \b[Neumann directions are tangent to the brane; Dirichlet directions are transverse to it.] The brane is dynamical: tangential massless open-string polarizations supply a gauge field, while transverse ones describe its displacement, as in <worldvolume fields from open-string massless states>. The unprojected bosonic brane also has a <tachyon>; the boundary-condition interpretation does not make that ground state supersymmetrically stable.
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