Shortly before midnight on New Year's eve, in one of the poorest and most racially diverse districts of Sweden, 15-year-old Samir Ardiwan was shot repeatedly in the chest and head. Amid the fireworks and celebrations, his death was at first barely noticed.

The murder was one of six since late December in Malmö, Sweden's third-largest city, which has led to the biggest police investigation in the country's history since prime minister Olof Palme was assassinated in 1986.

The violence follows a spate of racially motivated shootings in the city two years ago. The chief suspect in these attacks, Peter Mangs, was applauded by Anders Breivik, the rightwing extremist on trial for killing 77 people in Norway, as one of the "heroic young people" who should be celebrated for sacrificing their lives for the "conservative revolution".

  Right-wing extremist Anders Behring Breivik applauded racially motivated killings

The police believe the latest bout of violence stems more from gang wars than racial motivations, but the killings have shone a spotlight on an area of Sweden bubbling with racial and social tensions. It has prompted a fierce national debate in a country that prides itself on equality and tolerance.

For many, the poor and overcrowded estate of Rosengård, where Mr Ardiwan was shot and three suspects for his murder arrested, epitomises the country's failure to integrate its newest immigrant communities into mainstream Swedish society.

Of the 22,000 inhabitants of the towering concrete estate, built in the 1960s four kilometres outside the city centre, about 90 per cent are first- or second-generation immigrants, increasingly from Iraq, Afghanistan and Somalia. Unemployment is close to 40 per cent - five times the figure for the country as a whole. Two-thirds of its children live in relative poverty, defined as an income 60 per cent less than the national average.

The estate has a long history of racial problems. Bejzat Becirov, head of the local Islamic centre, said his mosque has been attacked 300 times since it was built in 1984, including two firebombs in the last 10 years. The surrounding area is the heartland of the far-right Sweden Democrat party, which won its first parliamentary seat in the last election.

According to Juan Havana, a musician of Chilean descent who runs a local youth centre, racial prejudice is part of the problem today, making it harder for those with non-Swedish names to get jobs. Unemployment then leads to social problems: "I know kids who are now putting on bullet-proof vests every day instead of their hoodies," he said.

It is not only locals trying to explain the problems in Rosengård. "This country has not been very good at integrating some immigrant communities, and that has to improve," said Jacob Wallenberg, an influential business leader whose family owns a controlling stake in important Swedish companies including Electrolux and Ericsson.

"There are pockets of unintegrated immigrant communities markedly in a few places in Sweden such as Malmö, Stockholm, Gothenburg and beyond," he said, adding that youth unemployment - higher than the European average at 23 per cent and a hot political issue - was part of the problem.

Other commentators have pointed to more structural factors. They say immigrants who came to Sweden in the 1960s and 1970s integrated more successfully because they were invited in to fill manufacturing jobs. But the second wave in 1990s and 2000s were mostly asylum seekers - such as the Iraqis who are the biggest ethnic group in Rosengård - let into a country where many of these low-skilled jobs had disappeared.

The violence in areas such as this, only a 20-minute walk from the richest areas of Malmö, has also prompted a debate about growing inequality in Sweden. Sweden has seen the steepest increase in inequality during the past 15 years among the 34 OECD nations, with disparities rising at four times the pace of the US.

Ehsan Noroozi, host of a local youth-orientated show called Your Street, said people in the poorer neighbourhoods of Malmö feel they are being left behind by an increasingly globalised world. He points to the EUR1.4bn European neutron research centre being built nearby in Lund: "How is that going to help us?"

Accusations of inequality are particularly sensitive in Sweden as few societies have defined themselves by their welfare-driven economic model as much as the Swedes. "Many feel this is a major pillar of Swedish identity that is being lost with potentially severe consequences," said Michael Forster, a senior analyst at the OECD.

So far around 20 people have been arrested for the half-dozen shootings in Malmö from December. The local police force has been doubled and more armed officers patrol the streets. But the family of Mr Ardiwan told local paper Aftonbladet in April that, while they were happy arrests had been made, none of it would bring their fifteen-year-old boy back.