Is it possible to have schizophrenia with no positive symptoms but just negative ones?

Yes. The many proposed causes of this disease can be modified by many variations in the body. So each person with this disorder can have a number of presentations. For example, an infection may alter genetic action and cause an uneven presentation of clique symptoms. Also many medications drop positive dramatic troubles, but negative ones require more help.
Yes. It is possible to have schizophrenia with just negative symptoms. Negative symptoms such as blunt affect and poverty of speech have a great effect on a person's quality of life.