  We report effects of electron-electron (\emph{e-e}) interaction on electron
spin resonance (ESR) in perpendicular magnetic field in two-dimensional (2D)
systems with Bychkov-Rashba spin splitting induced by spin-orbit interaction
(SOI) and structural inversion asymmetry (SIA). Using the Hartree-Fock
approximation, we demonstrate that the SIA results in non-zero many-body
corrections to the ESR energy and the energy of spin wave excitations. We
discover that the \emph{e-e} interaction in 2D systems with SIA not only can
enhance the ESR energy but can also lead to the ESR energy reduction. The
magnitude of this effect exhibits remarkable features in a wide range of
parameters relevant to experiment: it is found to be rather sensitive to the
sign of g-factor and the filling factor of Landau levels $\nu$. We derive
analytical expressions for many-body corrections to ESR energy and the
dispersion of spin wave excitations for the case of $\nu\leq 2$. We have found
out that \emph{e-e} interaction does not affect the ESR energy in the case of
filling of the lowest Landau level ($\nu\leq 1$) in 2D systems with positive
g-factors even at arbitrarily large values of Bychkov-Rashba constant. The
many-body renormalization of ESR energy in the case of fractional Quantum Hall
effect is also discussed.
