What is the power generating capacity for an airport GPU?
Power requirements are dependent on airframe and configuration (see this question for a general idea). GPU's come in varying sizes for varying aircraft types. For example this GPU (arbitrarily chosen) can deliver: 800 amps continuous, 2500 amps peak. While this GPU can only drive 70Amps continuous. Others may be able to drive more and some may drive less. Are you asking about a particular application? The GPU's at the tiny airport I fly out of that we use to bump start the occasional Piper are no where near the capacity of what you may find at JFK for starting up a 747.  


  Would it by possible to power GPUs entirely by solar power?


Depends on the application but it would be unlikely to chose such a medium for powering a GPU the way things stand now (in terms of power requirements). You may be able to have a battery powered GPU that is charged by solar cells but that would only work well in the smaller scenario. Having a solar powered airport that can provide ground power is a whole different question.