  The paper explores a theoretical possibility of resonant amplification of
electromagnetic modes generated by a nonlinear effect in Euler-Heisenberg
electrodynamics. Precisely, we examine the possibility of the amplification for
the third harmonics induced by a single electromagnetic mode in radiofrequency
cavity, as well as the generation of signal mode of combined frequencies
induced by two pump modes ($\omega_1$ and $\omega_2$) in the cavity. Solving
inhomogeneous wave equations for the signal mode, we formulate two resonant
conditions for a cavity of arbitrary shape, and apply the obtained formalism to
linear and rectangular cavities. We explicitly show that the third harmonics as
well as the mode of combined frequency $2\omega_1 + \omega_2$ are not
resonantly amplified while the signal mode with frequency $2\omega_1 -
\omega_2$ is amplified for a certain cavity geometry.
