Existence of capacity solution for a nonlocal thermistor problem in Musielak-Orlicz-Sobolev spaces

In this work, we study the existence of a capacity solution for a nonlocal thermistor problem in Musielak-Orlicz-Sobolev spaces. We get the existence of capacity solution using the approximate techniques and we prove the existence of a weak solution by introducing a sequence of approximate problems converging in a certain sense to a capacity solution. As a consequence, we obtain the existence of a capacity solution of the original problem in Musielak-Orlicz-Sobolev Lebesgue spaces.