COLUMN ONE : David and Goliath in Caucasus : Feisty Karabakh Armenians are defying the odds in a battle to liberate their tiny enclave from Azerbaijan. The key to their success? 'This is a war for our existence,' one veteran says.

Sitting around a headquarters picnic table in post-battle glow, the more seasoned, bristle-bearded Armenian fighters of the Nagorno-Karabakh Defense Army were struck anew by the contrast between themselves--mostly men in their 30s--and their enemies.

The picture, inscribed "To my brother, Elman," was on the body of an Azerbaijani tank crewman. It was dated just two days earlier and showed a group of dark-eyed teen-agers in uniform, some smiling with a hint of youthful cockiness. Most were probably gone now, blown away in the firefight.

It had been a good day's battle. Azerbaijani forces had attacked at dawn. The Armenians, pretending to retreat in disarray, had led them into a booby-trapped village, then savaged them with artillery.

AGDAM, Azerbaijan — They found the photo in one of the Azerbaijani tanks they had captured and took it as a war trophy.

"They're all so young," headquarters commander Grigory Gasparyan mused. "They just get sent into the meat grinder. . . . This is the third time we've seen them fire on their own soldiers to keep them from retreating."

No one needs to fire on the Karabakh Armenians to keep them from retreating. Unlike the young soldiers they face--who are handicapped by shaky training and low morale, they have a sense of purpose.

This is their corner of the Caucasus Mountains, populated mainly by Armenians for centuries. They see themselves as a national liberation army destined to free Karabakh from the Azerbaijani rule imposed by the Kremlin in the 1920s.

"This is a war for our existence," Gasparyan said. "The difference is in what you do and what you do it for. You know a few miles back is your family, children, women and old people, and therefore you're duty-bound to fight to the death so that those behind you will live."

That would seem to be the key to one of the greatest success stories by a military underdog since 1948, when tiny Israel held off the might of a dozen Arab nations surrounding it; a tough people, faced with what they see as the threat of extinction, get tougher.

The Armenians of Nagorno-Karabakh now number about 120,000--fewer than the population of Pasadena--and their mountainous enclave within Azerbaijan is about the size of Ventura County. They export mainly wine. They get some backing from their 3 1/2 million ethnic brethren in Armenia proper, but the real fight to control Nagorno-Karabakh, which began when they tried to secede from Azerbaijan in 1988, is theirs.

The Azerbaijanis, whom they have battled for six years in the former Soviet Union's longest war, number 7 million and are blessed with oil fields so rich that world petroleum powers are hovering in their capital, Baku, in hopes of winning a stake.

But for at least the last two years, the Karabakh Armenians have been winning--and then some.

In 1992, the Karabakh Armenian army, which is believed to have 10,000 to 20,000 men, cut a corridor through the slice of Azerbaijani territory that separates their enclave from Armenia. Then, last year, it managed to capture about 10% of Azerbaijani territory. Casualty counts routinely put Azerbaijani losses at five to 10 times greater than the Armenians', with combined deaths estimated at well over 15,000, including civilians.

Stepanakert, the Karabakh capital, runs under a wartime regime, but it runs. Every man age 18 to 45 is in the army. All power is centralized in the State Defense Committee. Food supplies allow each resident 15 pounds of flour per month. Thanks to the capture of a power plant, there is electricity most of the time--far more than can be said for Yerevan, the capital of Armenia.