We discuss a number of analytical studies, aimed at adding the influence of oscillations experienced by a pulsar/magnetar on its plasma magnetopshere. We show that particular modes of oscillations may considerably increase the pulsar/magnetar luminosity and apply the obtained theoretical results on the plasma magnetosphere of oscillating and rotating neutron stars
i) to propose a qualitative model for the explanation of the phenomenology of intermittent part time pulsars,
ii) to study the conditions for radio emission in rotating and oscillating magnetars by focusing on the main physical processes determining the position of their death lines, i.e. of those lines that separate the regions where the neutron star may be radio loud or radio quiet,
iii) to explain the subpulse drift phenomena adopting the space-charge limited flow model and comparing the plasma drift velocity in the inner region of pulsar magnetospheres with the observed velocity of drifting subpulses.