The technique for analytical investigation of the Alfvén resonance, proposed
by Dmitrienko [J. Plasma Phys.57, 311 (1997); 62, 145 (1999)] is used to
obtain the matching conditions and to calculate the rate of resonant absorption
and heating in a nonlinear dissipative resonance layer. It is shown that one matching
condition is the invariability condition for the coefficient of the singular part of
the solution describing the MHD mode outside the resonance layer, and the other
condition is a jump of the coefficient of a regular solution, the value of which depends
on the ratio of the dissipative to nonlinear spatial scales. It is established that
the ratio of the jump of the imaginary part of the regular solution to the coefficient
of the singular solution is exactly equal to the rate of resonant heating, and this
heating is calculated as a function of the ratio of the linear dissipative to nonlinear
scales. The resonant absorption coefficient is calculated as well. It is shown that the
nonlinearity leads to a decrease of the heating rate and the absorption coefficient
compared with those predicted by linear theory.