  The equations of secular evolution for dust grains in mean motion resonances
with a planet are solved for stationary points. This is done including both
Poynting-Robertson effect and stellar wind. The solutions are stationary in
semimajor axis, eccentricity, and resonant angle, but allow the pericentre to
advance. The semimajor axis of stationary solutions can be slightly shifted
from the exact resonant value. The periodicity of the stationary solutions in a
reference frame orbiting with the planet is analytically proved. The existence
of periodic solutions in mean motion resonances means that analytical theory
enables for dust particles also infinitely long capture times. The stationary
solutions are periodic motions to which the eccentricity asymptotically
approaches and around which the libration occurs.
  Using numerical integration of equation of motion are successfully found
initial conditions corresponding to the stationary solutions. Numerically and
analytically determined shifts of the semimajor axis form the exact resonance
for the stationary solutions are in excellent agreement.
  The stationary solutions can be plotted by locations of pericenters in the
reference frame orbiting with the planet. The pericenters are distributed in
the space according to properties of dust particles.
