Papa John's lackluster performance during the third quarter was expected, but a smaller decline in same-store sales and renewed excitement about a possible sale sent shares up nearly 6 percent Wednesday.

A feud with founder John Schnatter that started in July has thrown the company into turmoil. Sales have remained elusive as fewer customers are buying pizzas from the chain and franchisees have been torn between the old regime and the new one.

While same-store sales were not as poor as expected, they were still down nearly 10 percent in the quarter, raising questions about if Papa John's can really initiate a turnaround or if an acquisition is the best route to recoup losses.

"Papa John's posted another eventful quarter, while challenges clearly remain, there were some encouraging signs as sales trends improved late in the quarter," Peter Saleh, analyst at BTIG, wrote in a research note Wednesday. "The improvement and positive commentary on October supports a better sales outlook for [fourth quarter 2018] and into 2019, though we are not convinced the concept is out of the woods quite yet."

The pizza chain's sales improved in September over the previous two months, the company said in releasing its third-quarter earnings Tuesday. Executives credited the improvement, in part, to a new ad campaign that replaced Schnatter's image with other employees and franchisees in the company. As the company's official spokesman, Schnatter's image covered Papa John's pizza boxes and he represented the company in commercials.