Sure you can still succeed. All you have to do is be better than your competitors. Every business has some sort of shortcomings/lacking. You have to take advantage of these lacking of your competitors to make your business better/superior than them. You need to provide better service, quality products and competitive pricing to your customers. You need to offer something different than what your rivals are offering. Once you establish yourself and build a good reputation, you will be easily able to survive the market.
Nowadays, most people become great business men or women because of the competitors they have around them. Without competitors, they might hardly become successful in their business. Competitors always bring more seriousness in different ways, not only in the business aspect. When people have competitors, they often become more serious about their lives.
I know a businessman who owns a provisions store near our house. It was the only provisions store in the area, so he was less serious; sometimes, he wouldn't come to the store on time, and even if some items ran out, he wouldn’t be in a hurry to restock. However, when other provisions stores started opening in the area, he became more serious, and he even went on to open a supermarket. Having competitors can motivate people to become serious and succeed in life.