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We present analytical and numerical studies of pinned superconducting statesof open-ended Josephson ladder arrays, neglecting inductances but taking edgeeffects into account. Treating the edge effects perturbatively, we findanalytical approximations for three of these superconducting states -- theno-vortex, fully-frustrated and single-vortex states -- as functions of the dcbias current $I$ and the frustration $f$. Bifurcation theory is used to deriveformulas for the depinning currents and critical frustrations at which thesuperconducting states disappear or lose dynamical stability as $I$ and $f$ arevaried. These results are combined to yield a zero-temperature stabilitydiagram of the system with respect to $I$ and $f$. To highlight the effects ofthe edges, we compare this dynamical stability diagram to the thermodynamicphase diagram for the infinite system where edges have been neglected. Webriefly indicate how to extend our methods to include self-inductances.Comment: RevTeX, 22 pages, 17 figures included; Errata added, 1 page, 1  corrected figur

Superconducting states and depinning transitions of Josephson ladders