In a league full of problem franchises, the North American Soccer League's most prominent eyesore plays in the city that wrought the league's first true success story seven years ago: Philadelphia.

The Philadelphia Fury has been in operation for three seasons. It has 15 owners, has had four coaches, changed its name from Furies to Fury five minutes before announcing the franchise's existence, and drew about the same number of fans last season that the Cosmos drew in one game -- Soccer Bowl '78.

Now the various owners, who have lost about $3.1 million since purchasing the franchise, are looking for a buyer. "Some of us want to stay involved," one of the owners, Larry Levine, said last week. "But we need some new capital in the club."

Levine said four groups are interested, at least one wanting to buy the club outright. But meantime, as negotiations drag, the current owners -- who include music start Peter Frampton and Paul Simon -- won't spend any money on the team. They won't promote, they won't advertise and they won't spend money on players.

Caught square in the middle of the situation is Coach Eddie Firmani, hired prior to the season, supposedly to rebuild a 10-20 team.

"At times it's been frustrating," Firmani admitted. "If the money were there we could have some very good players here quite quickly.

"I hope we're going to get new ownership soon. If that happens, I think things will work out." And if not? "I'll just have to keep working, I guess," Firmani said.

An example of Firmani's frustration is Ossama Khalil, a skilled Egyptian player who has trained with the Fury for several weeks. But the club can't sign him because his team back home is asking a $200,000 transfer fee (not very high by today's standards) and the owner's aren't willing to pay that kind of money.

So the Fury limps along with a 1-5 record and continues to draw crowds such as the announced 2,478 (which looked like fewer than 1,000) that showed up Wednesday for a game against the Chicago Sting.

"I can remember when this really was a soccer town," said Fury goalie Bob Rigby, the keeper for the expansion Philadelphia Atoms when they won the 1973 NASL title and averaged almost 15,000 per home game. "We did things right in that organization and the fans responded.

"If Eddie had the money he'd have a tough team over here on the field in a week. But now, all we can do is wait, and hope things get better. It's kind of depressing."

A sad story for a league desperately in need of some new success stories.

Another note from the category of dubious league priorities: A publicity man for one of the league's failing franchises called the league office last week and, at one point, asked what the news was in New York and around the league.

"Well," the league man said excitedly, "Arsenal pulled out of the Challenge-Cup but we got Manchester City to replace them."

"Great," said the PR man. "Now would you mind telling me how we've supposed to make our payroll next Friday?"

The Trans-Atlantic Challenge Cup is finally set, at any rate. The four participating teams will be the Cosmos, Vancouver, Manchester United and Roma of Italy. The foreign teams will play in Giants Stadium and in Vancouver May 21 and 24. The cup will be a round-robin affair with two points awarded for a win and one point for a tie. Goal differential will break any times at the end. The cup will culminate with a Memorial Day doubleheader in Giants Stadium, Roma played Manchester followed by the Cosmos and Vancouver in a rematch of their classic 1979 playoff, won by the Whitecaps.

Giorgio Chinaglia's seven goals in the Cosmos' first seven games gives him 101 for his NASAL career, tying Ilija Mitic for the all-time league goal-scoring record. He can break the record today against Memphis in Giants Stadium.

If you were wondering about the Minnesota Kicks' 1-4 start after four straight division championships: the Kicks, by a scheduling quirk, played their first five games on the road. Last year 14 of their 21 victories came at home . . . Proof that indoor soccer and outdoor soccer are different games: Atlanta's David Byrne, leading NASL scorer during indoor season, can't make the Chiefs' traveling squad and wants to be traded. The Chiefs continue to flounder at the gate -- 3,100 was the announced crowd Wednesday -- The Seattle Sounders' outstanding 6-1 start must be credited largely to the goalkeeping of former Cosmo and Tulsa Roughneck Jack Brand. He has six shutouts . . . Alan Green's six goals for 12 points puts the Diplomat striker in fifth place in league scoring. Ray Hudson of Fort Lauderdale leads with 18 points.