Are we talking about containers or on the ground as in a raised bed where some soil will be available?

Whether or not additional nutrients will be needed will depend on the quality of the compost. Several micro-nutrients normally provided by soil or additions to container mixes are needed for tomatoes and other vegetables that straight compost may or may not provide.

Can I ask why straight compost is your choice for a growing medium instead of a more standard approach?

Dave

vinnie:
I too use 100% compost, added to each spring. My garden is naturally building up and creating a neat looking berm in the winter. I cover crop in the fall and turn it over in the late January.
I do use a solution of fish emulsion and sometimes seaweed extract right before the really scorching heat hits. Other than that the soil keeps a ph level of 7.5 , and copious amounts of NPK.