Dexia, a Franco-Belgian bank that specializes in lending to local governments, got a $9.2 billion injection of capital to stave off imminent collapse after a loss of public confidence led to a 30 percent decline in its stock price Monday, according to announcements from the French and Belgian governments. It was the fifth time in recent days that European officials have had to respond to a crisis at one of their financial institutions, abruptly ending the confidence European officials displayed as recently as last week that their financial system was not as endangered by the troubled mortgage loans undermining the U.S. system. With the pace and scale of events seeming to quicken, the Irish government guaranteed the debt of six financial companies amid a sell-off of bank stocks, and European officials discussed possible broader action to address problems with the global financial system.