ABSTRACT
Consider a nonlinear problem of the so-called Duffing oscillator in space (see Kahn and Zarmi [11], page 198) governed by
w′′(x) + w(x)− w3(x) = 0, w(0) = w(L) = 0, (6.1)
where x is a spatial variable, w(x) is a real function of x defined in the region 0 ≤ x ≤ L, and the prime denotes the derivation. Obviously,
w(x) = 0
satisfies all of the above equations and thus is one of its solutions. However, for some values of L, there exist nonzero solutions so that the so-called simple bifurcation occurs.
