  In the present research, a variational technique to modifying the Poisson
equation is presented, expanding its modelling capabilities to include a wider
range of physical processes and resonant structures. The study examines the
implications of this modified equation to further develop our knowledge of
electrostatic potentials and providing a nonlocal extension of Einstein's
theory of gravitation, energy conversion and communication, in addition to the
methodological advancements. In addition to providing insights into the
dynamics of gravitational potential in systems exhibiting radial vorticity
fluctuation, the paper clarifies nonlocal effects, examines longitudinal
electromagnetic wave generation, and resonant phenomena in dusty plasma media.
