  We investigate emission of the bremsstrahlung photons in the scattering of
protons off nuclei at the $\Delta$-resonance energy region. Including
properties of $\Delta$-resonance in the nucleus-target to the bremsstrahlung
model, we find the following. (1) Ratio between incoherent emission and
coherent emission is about $10^{6}$--$10^{7}$ for $p + \isotope[197]{Au}$
(without $\Delta$-resonance) at energy of proton beam $E_{\rm p}$ of 190~MeV,
where the calculated full bremsstrahlung spectrum is in good agreement with
experimental data. This confirms importance of incoherent processes in study of
$\Delta$-resonances in this reaction, which have never been studied yet. We
estimate coherent and incoherent contributions, electric and magnetic
contributions, full bremsstrahlung spectra for the scattering of protons on the
\isotope[12]{C}, \isotope[40]{Ca}, \isotope[208]{Pb} nuclei at $E_{\rm
p}=800$~MeV, we find conditions for the most intensive bremsstrahlung emission.
(2) Transition $p\,N \to \Delta^{+} N$ in the nucleus-target reinforces
emission of bremsstrahlung photons in that reaction at $E_{\rm p}=800$~MeV.
Difference between the spectra for normal nuclei and nuclei with included
$\Delta$-resonance is larger for more light nuclei, but the spectra are larger
for heavier nuclei. (3) Taking into account shortly lived state of
$\Delta$-resonance, we find that the spectrum with $\Delta$-resonance in the
nucleus-target is essentially larger in the high energy photon region than the
spectrum without this $\Delta$-resonance (corresponding calculations for
\isotope[12][\Delta]{C}, \isotope[40][\Delta]{Ca}, \isotope[208][\Delta]{Pb} in
comparison with \isotope[12]{C}, \isotope[40]{Ca}, \isotope[208]{Pb} are
provided). Such an aspect is recommended for registration of
$\Delta$-resonances in nuclei in possible future experiments.
