Can one apply rogaine on the side of their hair?

Minoxidil works by widening the hair follicle, causing a thicker strand of hair, and by prolonging the anagen stage of hair growth which results in longer and a higher number of hair strands. 

There are two strengths of minoxidil: 2 percent and 5 percent. The 5 percent has been shown to be more effective without a significant increase in irritation or other side effects. Both strengths are applied to the dry scalp twice a day. It is important to know that the treatment must be continued. Although the drug is was only clinically tested in the vertex it will work any place its applied so you may continue to apply in the areas you are thinning. Typically men do not lose the hair around the sides and back, the donor area. I recommend you speak with a physician to ensure there isn't anything outside of male pattern baldness causing your hair loss. 

IF the cause of the hair thinning on the sides is androgenetic alopecia, this plan could make a lot of sense. However, if the hair loss is due to something else, this may not be the first consideration. Without photos or the opportunity to actually see the scalp up close, a diagnosis can't be given. 

It is fine to apply Rogaine to one side of the scalp. It does take time to see a result, so be patient.