Palo Alto Networks Inc. and Kayak Software Corp. raised a combined $351.4 million, pricing their initial public offerings above the proposed ranges and tapping renewed investor demand for technology shares.

Palo Alto, a maker of Internet firewalls, raised $260.4 million selling 6.2 million shares at $42 apiece, it said in a statement Thursday, after offering the shares for $38 to $40 each. Kayak, an online travel company, raised $91 million selling 3.5 million shares at $26 apiece, a dollar more than the top end of the marketed range.

Palo Alto and Kayak join scheduled IPOs this week from companies including Five Below Inc. and Fender Musical Instruments Corp., to mark the busiest week for U.S. initial offerings since March, according to data compiled by Bloomberg. Robust demand for the offerings follows a monthlong drought in the wake of Facebook Inc.’s disappointing May debut and may indicate renewed investor demand for companies that promise growth, according to Jayson Noland, an analyst with Robert W. Baird & Co.

“There’s an appetite for innovation and growth out there and there’s going to be a premium placed on growth, whether it’s tech or anywhere else,” said Noland by telephone. “We’ve seen a pretty steep discount on companies that are facing a secular decline.”

Palo Alto initially said it would offer the shares for $34 to $37 and raised the range this week. The stock will start trading Friday on the New York Stock Exchange under the symbol PANW.

Trading Friday

Kayak, which will trade under the ticker KYAK on the Nasdaq Stock Market, had planned to sell the shares at $22 to $25 apiece. The offering value’s Kayak at about $1 billion, based on its 38.6 million shares outstanding.

Palo Alto’s IPO price values it at about $2.8 billion, or almost 13 times sales of $220 million in the 12 months through April 30, Bloomberg data show. That’s double the average multiple of 6.4 for similar-sized peers such as Juniper Networks Inc. and Check Point Software Technologies Ltd. Larger competitor Cisco Systems Inc. trades at a multiple of 2, and Intel Corp. trades at 2.4 times.

Palo Alto’s offering follows the successful debut by ServiceNow Inc. last month, which opened the gates for other IPOs after the flop of Facebook’s $16 billion initial share sale froze the U.S. market for more than a month.

Emerging Force

While shares of Internet companies such as Facebook, Groupon Inc. and Zynga Inc. have declined since their IPOs in the past year, some technology firms that sell services and products to companies have fared better. In addition to ServiceNow, which sells technology-management software, Splunk Inc., a data-analytics company, has risen 72 percent since its IPO on April 18.

Palo Alto is an emerging force in the market for corporate anti-hacking technology, where its competitors include Cisco, Juniper Networks and Check Point Software Technologies. Revenue at the company, led by Chief Executive Officer Mark McLaughlin, has surged at least 57-fold since 2008 as more businesses invest to shield their networks from outside threats.

The company, founded in 2005, offered 4.69 million shares, while existing holders offered 1.5 million, regulatory filings show. Venture firms Greylock Partners and Sequoia Capital didn’t plan to sell shares and will own more than 41 percent of the company after the IPO, according to regulatory filings.

Over-Allotments

Palo Alto also said it has granted the underwriters a 30- day option to purchase up to an additional 930,000 shares of common stock to cover any over-allotments. Morgan Stanley, Goldman Sachs Group Inc. and Citigroup Inc. led Palo Alto’s share offering.

The company’s sales in the three months ended April 30 were $65.7 million, more than double the $31.2 million a year earlier, according to data compiled by Bloomberg. Net income in the nine months ended April 30 was $5.34 million, compared with a loss a year earlier, with sales for that period approaching $180 million, the company said in a filing.

The global market for enterprise network security may rise to $12.5 billion by 2015 from $10 billion this year, Palo Alto said in its filing, citing IDC.

Kayak, which first filed to go public in November 2010, is the first U.S. consumer Internet company to go public since Facebook’s IPO in May. Norwalk, Connecticut-based Kayak delayed its roadshow after Facebook shares tumbled.

Revenue at Kayak jumped 39 percent in the first quarter to $73.3 million, from $52.7 million a year earlier. The company reported net income in the period of $4.1 million, following a $6.9 million loss in the year-earlier quarter because of a writedown related to its SideStep brand.