A theoretical investigation is presented on the steady states of a planar plasma diode where static ions uniformly occupy the inter-electrode region. A cold and purely monochromatic electron beam is injected from the emitter plate, and the emitted electrons are carried to the collector plate through the uniform background of stationary ions. It is considered that the electrons suffer collisions with the other particles (with ions or neutral atoms) during its transportation through the inter-electrode gap. The effects of collisions are incorporated through a simplified one-dimensional model. With the help of Lagrangian description of fluid-Maxwell's equations, time-independent states are explored for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions are categorized into "Bursian" and "Non-Bursian" branches in "emitter electric field vs diode gap" parametric space. The Non-Bursian solutions are found to be very sensitive to the dissipative term as they only exist for small, non-zero values of the normalized collision-frequency. © 2018 Author(s).