NEW YORK -- Shares of Barnes & Noble Inc. (BKS) soared after activist investor Ronald Burkle sought to boost his stake in the company despite questions about how much value is left in the book retailer following recent struggles and increased competition in the publishing industry.

Burkle sent a letter to Barnes & Noble's board Thursday, seeking to acquire as much as 37% of the company, up from his current stake of 19%. He also blasted the company for having two sets of rules for its poison pill: one applying to insiders and one applying to other investors.

The billionaire and his investment firm, Yucaipa Cos., are seeking to raise their stake without triggering a shareholders rights plan adopted by the company in November.

Burkle's move comes at a particularly challenging juncture in the bookselling business. Barnes & Noble and other brick-and-mortar book retailers such as Borders Group Inc. (BGP) have suffered from declining sales as the economic downturn spurred a drop in retail traffic. Shoppers also have turned to online and discount booksellers, as well as to electronic books.

To help diversify and compete with Amazon.com Inc.'s (AMZN) popular Kindle device, Barnes & Noble launched its Nook e-reader late last year. It now also faces competition from Apple Inc.'s (AAPL) much anticipated iPad, and Google Inc. (GOOG) is expected to enter the fray later this year with its e-bookstore called Google Editions.

Goldman Sachs analyst Matthew J. Fassler said that despite any changes potentially brought by Burkle, Barnes & Noble still remains "structurally challenged" by eroding physical book sales, the likelihood of eroding loyalty program membership and increased marginalization in the e-reading arena.

"As such, we question the long-term earnings stream associated with the business, and believe that at its after-hours trading price, the stock is overvalued," Fassler said in maintaining his sell rating on the stock. Shares jumped 18% in late trading Monday after Burkle's filing with the Securities and Exchange Commission.

A representative from Barnes & Noble wasn't immediately available to comment.

In recent trading Tuesday, Barnes & Noble shares climbed 8.8% to $19.59 on heavy volume, up 21% over the past 12 months. In earlier trading, they rose as much as 16% to $20.85.

In his letter, Burkle said it was unfair for the Riggio family, which founded the company, to own 37% of the shares while no other shareholder can hold 20% without triggering the rights plan, or poison pill, designed to thwart any potential hostile-takeover effort.

The letter said the poison pill "hurts the share price and inappropriately penalizes Barnes & Noble's "non-Riggio" shareholders."

Goldman's Fassler said that while Burkle cites governance challenges at Barnes & Noble, he believes most of the company's perceived missteps are in the past and are essentially irreversible. The most notable was the purchase of the college business from Riggio for $596 million last year. The two companies had operated separately since Barnes & Noble went public in 1993.

"If successful, we believe the most significant potential changes to the business Mr. Burkle could bring include a reduction in capital expenditures and, potentially, the restructuring of obligations to Len Riggio associated with payment for College, possibly resulting in a return of more cash to shareholders," Fassler said.

(Jeffrey A. Trachtenberg and Kathy Shwiff contributed to this report.)