For the last two weeks, Prince George's County Executive Lawrence Hogan has spent countless hours behind the locked doors of his office, scribbling acerbic letters, railing against disloyalty and leaks on his staff and bitterly complaining about the "bum rap" he feels he is getting on his handling of an impending strike by 1,500 county employes.

In circumstances that might have disheartened and overwhelmed another executive, Hogan has flourished, thriving on the confrontation mode of politics that has made him one of the county's most popular politicians and the only current Republican elected to office in a solidly Democratic county.

While the approaching strike by the public employes union is a current example of this style, in the 16 months since he has become county executive Hogan has fought continually with the Democrats on the county council, the state legislators, the county school board, reporters, unions and just about anyone who has crossed his path.

All this, according to recent public opinion polls, has simply polished his popular image as the tough guy defending the little people against the excesses of government.

But in terms of running the county government the confrontation method has produced mixed results, some county officials believe. Hogan's plans often have been scrapped or substantially altered by his political opponents, and other efforts left in limbo while argument, public and private, rages.

"His style has always been more confrontation, look for the headline and don't worry about getting things done," said council chairman Parris Glendening, Hogan's chief critic who is a likely contender for county executive in 1982. "His problems with the [public employes] union is consistent with his style. He always tried to pit one group against another for his own advantage."

Said another council official: "His style is 'my way or no way' and that's it. There is no such thing as compromise."

Hogan defends his style as simply part of the Prince George's political tradition, where colorful rhetoric and biting comments govern all political debate. "I've always been a fighter," Hogan said. "And [as county executive] we've been able to get a lot of things done."

While Hogan points to some economies he has implemented in the cost of county government, efforts to attract more expensive housing and business to the county and a tax-rate decrease he soon will announce as part of next year's budget, as evidence of his sucesses as executive, his opponents point to what they consider to be serious failures.

Since he was elected, Hogan has lost the battle over what he described as his "most important appointment," that of police chief nominee James Taylor. He has also had the county council rebuff him on his major economic development program, change his first budget and prevent him from appointing new commissioners to some influential posts. In last year's legislative session in Annapolis, he failed to get a bonding bill through the legislature and lost several appointment prerogatives because of conflicts with state legislators.

Hogan and his aides say that his losses are purely the result of partisan politics, of all the Democrats in every other elective post in the county ganging up on the one elected Republican.

While many of those officials will admit that partisan differences have played a role in the fights, they also believe that Hogan could have avoided many of the losses if he was not so insistent on confrontation.

"In most of these cases, there's no reason Hogan had to lose," said one county council official. "But he has to react to every challenge to his ego and come out swinging regardless of what the consequences will be. He has never learned to pick his fights, he just fights all of them."

His current match of strength with the public employes union is, they say, a case is in point.

After his negotiators spend a year bargaining with the union, which represents some of the lowest paid workers in the county government, they finally reached a tentative agreement that was by all accounts quite favorable to the county. It granted the union members a 4.7 percent wage increase this year and 5 percent next year.

Hogan's aides have said they believe the county executive could have been persuaded to sign the agreement, with some minor revisions, if not for a newspaper article that quoted political rival Glendening warning Hogan that he may have committed an unfair labor practice in handling the negotiations.

When Hogan read that article, he blew up, refused to consider the tentative agreement and told his aides there was no way he would sign it if it would look as though he had capitulated to Glendening and the union, according to his aides.

Several days later, Hogan criticized his own negotiators, refused to talk to reporters, severely restricted access to the executive suite of officers and vetoed the contract, citing some economic provisions that union officials and even his aides admitted were minor.

Three days later, Hogan said he decided not to sign the agreement because it would have allowed for a fulltime, county-paid shop steward and county-paid leave for other union leaders. Shortly after that, the union notified the county it would strike on March 24, next Monday.

Hogan said recently that he would like to avoid a strike but it is up to the union to make the first conciliatory move. "I'm not going to capitulate because of public pressure," he said. In the meantime, he has unleashed a battery of legal maneuvers to at least delay the walk-out date, and sends out regular missives to union members warning them of the conquences of a strike.

Union officials have said they are convinced that Hogan wants a strike. "He thinks its good politics. His statements and his decisions defy all logic," said union representative Paul Manner, whom Hogan has refused to deal with ever since Manner supported Hogan's opponent in the county executive's race. "It's part of the whole confrontation style."

Glendening and other council members see a similar design behind Hogan's actions. "He wants a strike," said Glendening. "It's the union, in this case, against him and the taxpayers. But when you look at the [tentative agreement] in depth, you see what the real story is. He is causing the strike."

Although the tensions between Hogan and the council have increased during the union impasse, the county executive and his aides are confident that relations between Hogan and the county's other elected officials will improve before the end of his second year in office.

Hogan has spent more time in Annapolis with the state legislators this session and his aides have convinced him that he must spend more time with the county council or authorize someone in the executive's office to act as "the political mail carrier," to find out the needs of individual council members and let them know what Hogan wants.

"Bill Gullett [the county's other Republican county executive in the early 1970s], had the same problems in his first two years.It takes some time when you're coming from opposite sides of the political spectrum to work out turf," said one Hogan aide.

Said one council member recently: "Hogan's problem is that he has always used too much muscle. If he learns to rein it in he could have most of these people eating out of his hand."