  We prove the existence of critical points of the $N$-vortex Hamiltonian
  $H_\Omega (x_1,\ldots, x_N)
  =\sum\limits^N_{i=1}\Gamma^2_i h(x_i)
  + \sum\limits_{i,j=1\atop j\not= k}^N
\Gamma_i\Gamma_jG(x_i,x_j)+2\sum\limits_{i=1}^N\Gamma_i\psi_0(x_i)$
  in a bounded domain $\Omega\subset{\mathbb R}^2$ which may be simply or
multiply connected. Here $G$ denotes the Green function for the Dirichlet
Laplace operator in $\Omega$, more generally a hydrodynamic Green function, and
$h$ the Robin function. Moreover $\psi_0\in C^1(\overline\Omega)$ is a harmonic
function on $\Omega$. We obtain new critical points $x=(x_1,\dots,x_N)$ for
$N=3$ or $N=4$ under conditions on the vorticities $\Gamma_i\in{\mathbb
R}\setminus\{0\}$. These critical points correspond to point vortex equilibria
of the Euler equation in vorticity form. The case $\Gamma_i=(-1)^i$ of
counter-rotating vortices with identical vortex strength is included. The point
vortex equilibria can be desingularized to obtain smooth steady state solutions
of the Euler equations for an ideal fluid. The velocity of these steady states
will be irrotational except for $N$ vorticFity blobs near $x_1,\dots,x_N$.
