* Apple rises 1.4 percent as new iPhone unveiled
* German court decision on bailout fund lifts stocks
* Facebook's stock gains after Zuckerberg comments
* Indexes up: Dow 0.07 pct, S&P 0.21 pct, Nasdaq 0.32 pct
By Wanfeng Zhou
NEW YORK, Sept 12 (Reuters) - Wall Street ended little changed on Wednesday, erasing early gains, as investors turned cautious before a Federal Reserve decision on another round of monetary stimulus to boost the economy.
Stocks got a lift early after Germany's Constitutional Court approved the new euro zone rescue fund, which will allow the European Central Bank to buy sovereign bonds in an effort to reduce crippling borrowing costs faced by Spain and Italy.
But the gains faded as investors shifted their attention to the Fed, which concludes a two-day meeting on Thursday. Equities have rallied on expectations of more Fed action to keep interest rates low, leading some analysts to warn of disappointment.
Economists put the odds of a third round of bond buying from the Fed at 65 percent, up from 60 percent in August, according to a Reuters poll.
"The market is somewhat nervous ahead of tomorrow's Fed decision, and rightfully so," said Peter Cardillo, chief market economist at Rockwell Global Capital in New York, who believes the Fed will not begin another round of stimulus until after November's presidential election.
"We could be setting ourselves up here for a quick 2 to 4 percent correction."
The Dow Jones industrial average closed up 9.99 points, or 0.07 percent, to 13,333.35. The Standard & Poor's 500 Index ended up 3.00 points, or 0.21 percent, to 1,436.56. The Nasdaq Composite Index gained 9.79 points, or 0.32 percent, to 3,114.31.
Apple Inc shares were up 1.39 percent to $669.79 after it unveiled its iPhone 5. The introduction of the new iPhone comes as Apple tries to fend off competition that has reached a fever pitch.
Facebook Inc jumped 7.7 percent to $20.93 after Chief Executive Mark Zuckerberg hinted at new growth areas from mobile to search in his first major public appearance since the No. 1 social network's rocky IPO in May.
The S&P 500 index has advanced more than 9 percent since the start of June on hopes for global central bank stimulus. The index has been unable to break through the 1,438-1,440 level, seen as a significant resistance point.
Uncertainties about the economic outlook, highlighted by recent profit warnings from FedEx Corp. and Intel Corp. , could also limit the market's upward momentum.
"It's a little scary for me when you think about what we are going to be faced with next year," said Catherine Avery, president of Catherine Avery Investment Management in New Canaan, Connecticut.
"In addition to the fiscal cliff, we do have a very slow rate of GDP growth. It's very possible that the S&P earnings that analysts are predicting for next year are just way too high."
Ford Motor's stock was up 0.59 percent to $10.21 after the company's board of directors decided to discuss this week a succession plan for Chief Executive Alan Mulally, who is expected to retire by the end of 2013, Bloomberg reported on Tuesday, citing a person familiar with the matter.
Chesapeake Energy slipped 1.04 percent to $19.89 after the company said it is selling $6.9 billion in gas fields and pipelines, with most of its assets in the Permian Basin being sold to Royal Dutch Shell Plc and Chevron Corp , as well as most of its remaining infrastructure network.
Mediware Information Systems Inc shares surged 39 percent to $21.86. The clinical software solutions provider agreed to be acquired by private equity firm Thoma Bravo LLC for $22 per share in cash.
On the New York Stock Exchange, about two stocks rose for every one that fell. On the Nasdaq, three stocks rose for every two that fell.
Volume was light, with about 6.15 billion shares traded on the New York Stock Exchange, the American Stock Exchange and Nasdaq, below last year's daily average of 7.84 billion.