finite interval of $u$ but negative for $u \rightarrow \pm \infty$, all solutions of (26) which are positive definite everywhere have positive curvature for $u \rightarrow \pm \infty$ and are not compatible with the boundary conditions as given by (37). This merely reflects the fact that (26) describes the distribution $\Phi(u)$ only in the finite interval $u_1 \leq u \leq u_2$, in which $\Phi(u)>0$. The same was found to be true for $b=0$ in the last section. From (37) in combination with (32), $\Phi(u)$ has to vanish for $u \rightarrow \pm \infty$, and can be positive for finite $u$. As follows from minimizing the free energy functional $\gamma$ (14), the solution $\Phi(u)$ has to be smooth everywhere and thus fulfills $\Phi(u)=\Phi'(u)=0$ at the two boundaries $u=u_1$ and $u=u_2$.

Now the following statements can be made: a) There have to be intervals of $u$ where $\Phi(u)$ has negative curvature in order to fulfill the boundary conditions $\Phi(u)=0$ at $u=u_1$ and $u=u_2$; b) close to the boundaries $u=u_1$ and $u=u_2$, the curvature has to be positive in order to fulfill $\Phi'(u)=0$ at $u=u_1$ and $u=u_2$; c) consequently, the solution $\Phi(u)$ crosses $h(u)$ at two values of $u$ inside the region bounded by 