Abbey:  Thanks for your question.  From your pictures, it does look like your plants may be suffering from verticillium wilt.  You should confirm this by sending samples to the Penn State Plant Disease Clinic (https://plantpath.psu.edu).  This is a free service and they can provide a definitive diagnosis.  If this is verticillium wilt, there is no cure.  The recommendation is to remove the plants and dispose of in the trash (not the compost).  Also, as the fungus can persist in the soil for many years, it is advisable to solarize the area to reduce concentrations.  Covering the area where the plants were with plastic (clear is best but black will do) and letting it bake in the summer sun for a couple of months may reduce concentrations sufficiently to allow planting the area next year with resistant crops.  I wouldn't plant anything in the nightshade family (tomatoes, eggplant and potatoes, or other particularly sensitive species) in this spot for at least a couple of years.  It will also help next year to select seeds or plants that are resistant to this disease.  I have attached a Fact Sheet with additional information.  Please let me know if you have any questions or concerns.