  We study equilibrium solutions for the problem $u_t={\epsilon}^2 u_{xx} -u^3
+\lambda u -cos(t)$,$u_x(0,t)=u_x(L,t)=0$. Using a shooting method we find
solutions for all non-zero $\epsilon .$ For small $\epsilon $ we add to the
solutions found by previous authors, especially Angennent, Mallet-Paret and
Peletier, and Hale and Sakamoto, and also give new elementary ode proofs of
their results. Among the new results is the existence of internal layer-type
solutions. Considering the ode satisfied by equilibria, but on an infinite
interval, we obtain chaos results for $\lambda \geq \lambda
_{0}=\frac{3}{2^{2/3}}$ and $0<\epsilon \leq {1/4}.$ We also consider the
problem of bifurcation of solutions as $\lambda $ increases from $0.$
