When you say "lengths" you mean the total length of all three sides, right? An isosceles triangle has two sides of equal length and another side. Calling the two equal lengths "x" and the third side "y", the total length is 2x+ y so you are looking for all possible integers x and y such that 2x+ y= 1994. So y= 1994- 2x= 2(997- x) which means that y must be an even number.
In order to have 3 sides, x and y must be positive (not 0) so x can be any integer from 1 to 996 which then gives a unique value for y.