We consider the Gierer-Meinhardt system in R^1.
where the exponents (p, q, r, s) satisfy
1< \frac{ qr}{(s+1)( p-1)} < \infty, 1 <p < +\infty,
and where \ep<<1, 0<D<\infty, \tau\geq 0,
D and \tau are constants which are independent of \ep.
We give a rigorous and unified approach to show that the existence and stability of N-peaked steady-states can be reduced to computing two
matrices in terms of the coefficients D, N, p, q, r, s. Moreover, it is shown that N-peaked steady-states are generated by exactly two types of peaks, provided their mutual distance is bounded away from zero
