New Hampshire Democrats tonight sent Sen. Edward M. Kennedy home to Massachusetts empty-handed, giving a solid victory in their primary to President Carter, the candidate they had last seen 10 months ago.

Carter defeated Kennedy in the primary by 11 percentage points, leaving the challenger to wonder where or when he could find ground on which to continue his underdog campaign.

Kennedy has a near-guaranteed victory next Tuesday in Massachusetts, but after that there is nothing but trouble -- a run of primaries and caucuses from the Deep South to the Far West with a nearly empty treasury and a bagful of issues that have failed to take hold.

Californiaa Gov. Edmund G. (Jerry) Brown Jr., in even weaker condition after a distant third-place finish, said he will try to revive his candidacy a month from now in Wisconsin.

Final results showed Carter with 53,586, or 49 percent; Kennedy with $41,540, or 38 percent; Brown with 10,727, or 10 percent, and minor candidates splitting 3 percent.

White House press secretary Jody Powell pointed to the problem facing both the president's challengers when he said that, in the next three weeks, 14 states will begin the process of choosing 761 Democratic National Convention delegates.

Having failed to beat Carter in three widely separated contests in Iowa, Maine and New Hampshire, where he could concentrate his workers and financial resources, Kennedy and Brown now risk being run over by a Carter machine that has rarely looked more impressive than it did here today in Kennedy's back yard.

In winning the New Hampshire primary, Carter showed across the board strength.

The president captured Manchester, the state's largest city, by a margin equal to his statewide majority. He won the rural areas by a wider majority, and beat Kennedy by 18 points among blue-collar voters, according to ABC news.

Carter ran even with Kennedy among Roman Catholic voters and trailed his principal challenger only in some of the towns along the Massachusetts border.

In determinedly optimistic comments to supporters at his headquarters here, Kennedy vowed to "continue this campaign, on to Massachusetts, on to New York and Pennsylvania, and on to the Democratic convention."

Aides said they were heartened by Kennedy running closer to Carter than all of the publlished preelection polls had indicated, a fact they attributed to growing public concern over rising inflation rates.

Kennedy said, "The issues that were raised in New Hampshire are going to be the dominant issues for the primaries to come."

Carter backers were hoping for a big enough win to chill Kennedy's fund-raising and force an early exit from the contest. Privately, however, they were predicting that he would maintain his effort, on a reduced scale, for the next month and attempt a comeback in New York March 25.

Powell says the returns here were a measure of support for all the Carter policies Kennedy has challenged -- his handling of the Iran and Afghanistan crises and his domestic energy and economic measures.

Carter campaign chairman Robert S. Strauss told cheering supporters here that New Hampshire had sent "a signal to the world that this nation is united behind the president."

At the White House, Carter echoed that sentiment. "I think this return shows that the people of the country -- at least the ones in New Hampshire -- support the policies that we have espoused in international affairs, in our attempts to deal with the inflation issue and energy," he said.

Asked if Kennedy's candidacy was finished with the New Hampshire results, Carter replies, "No, I think that is a judgment for him to make. I would guess not."

Brown said the continuing preoccupation with international events had hurt his campaign. "We've lit another spark," he said, "but we've got a long way to go."

Brown was looking at a shutout in the delegate fight in New Hampshire. Under the Democratic Party's proportional representational formulas, Carter stands to gain 10 delegates and Kennedy nine from the day's voting.

But Kennedy desperately needed a win in his neighboring state to help raise funds for his campaign and to staff members and volunteers. And that he failed to get.

The Kennedy campaign has been limping financially since Carter routed the Massachusetts senator, 59 to 31 percent, in the Jan. 20 Iowa caucuses.

Kennedy staged enough of a comback Feb. 10 in the Maine caucuses to restart the flow of campaign cash. In Maine, Carter led Kennedy 43 to 40 percent in the popular vote and 46 to 38 percent in delegates.

Kennedy said after his Iowa defeat that he would have to win Maine and New Hampshire to remain a viable candidate, but he told reporters in the last few days that he would continue his underdog candidacy, no matter tonight's results.

Kennedy aides said that their campaign has spent money as fast as it has taken it in during the past month, but still has about $300,000 left from $1 million loaned to the campaign during the post-Iowa drought.

As much as any state in the country, New Hampshire symbolized the roller-coaster character of the 1980 Democratic race. Last September, a Boston Globe poll of the state gave Kennedy a 68-to-20 percent lead over Carter, with Brown having half as much support as the incumbent president.

At a Democratic picnic near here that month, there was far more activity around the table where a draft-Kennedy committee was collecting signatures than there was around the Carter-Mondale booth.

But when Kennedy became a declared candidate and began making frequent appearances here, problems quickly became apparent.

By Christmas, with the Iranian hostage crisis dominating the headlines, the three leaders of the draft camapign who had moved over as Kennedy's high command, Dudley W. Dudley, Joanne Symons and Dennis Kanin, were telling reporters that Kennedy would be hard-pressed to win here.

By late January, with the Soviet invasion of Afghanistan focusing more attention on Carter's foreign policy leadership, another Globe poll showed the president leading Kennedy by 56 to 31 percent.

Fate intervened time and again to keep Kennedy from focusing voters' attention on the economic issues that he had planned to put at the center of his campaign.

While inflation raced ahead unchecked, the shortage of fuel oil that some had feared never developed. And the mildest New England winter in 40 years reduced fuel requirements, easing the economic pinch and blunting Kennedy's attacks on Carter's policy of oil price decontrol.

On the final weekend of the campaign, when Carter was hit by the worst inflation news in six years and a fresh show of resistance to the release of hostages in Iran, his luck once again held. Instead of the news being dominated by those events, public attention was captured by the exploits of the U.S. Olympic hockey team and political conversations were dominated by the sudden controversy among Republicans over the noisy Ronald Reagan-George Bush debate in Nashua.

Meanwhile criticism of Kennedy mounted with the continued discussion of his role in the fatal Chappaquiddick accident in 1969 and his separation from his wife in recent years. Even though Joan Kennedy made several effective personal and television appearances on behalf of her husband, the most recent Globe poll showed an extraordinarily high 48 percent diapproval figure for Kennedy as an individual.

Acknowledging the seriousness of the problem, the Kennedy campaign switched its paid advertisements in the final days from criticism of Carter to defense of Kennedy's character delivered by his mother, Rose Kennedy, and his sister-in-law, Ethel Kennedy.

Through all these travails, however, the Kennedy organization did not quit, not even when post-Iowa financial problems cut off salaries for the paid organizers. In the final 10 days, Carter supporters conceded that Kennedy had more workers on the streets than they did.

The president's campaign was the mirror-image of Kennedy's. Carter made his last personal appearance in New Hampshire in April 1979, and it was not long after that when Chris Crown, a young New Mexican who had managed New Hampshire for Carter in 1976, came back to set up shop again.

In those early days, Carter's only ally in the state appeared to be Gov. Hugh J. Gallen, an old-fashioned politician who never forgot the help he got from the White House in his underdog 1978 campaign, and who never wavered in his backing for the president who had helped him.

With White House and statehouse patronage helping, Brown reactivated the Carter network and had an organization in place when public attitudes toward the president turned more favorable late in the year.

In the closing weeks of the campaign, the main goal of Gallen and the visiting Carter surrogates, led by Vice President Mondale and Rosalynn Carter, was to warn against the complacency induced by the one-sided polls.

Gov. Jerry Brown tried several approaches to New Hampshire, few of them sustained long enough to provide a real test of his appeal. A year ago, he came to the state to lobby for passage of a balanced-budget amendment to the U.S. Constitution, a stand that brought him into direct confrontation with Gallen and most of the Democrats in the legislature.

When he returned to the state briefly last fall, Brown seemed notably ill at ease. But after his relatively successful venture in the Maine caucuses, Brown tried to duplicate that effort here.