Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213120220301The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition397408550510.22075/ijnaa.2022.5505ENRaad AwadHameedDepartment of Mathematics, College of education for pure science, Tikrit University, IraqMaan A.RasheedDepartment of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraqhttps://orcid.org/00Hekmat Sh.MustafaDepartment of Mathematics, College of Education, Al- Hamdaniya University, Mosul, IraqFaez N.GhaffooriDepartment of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, IraqJournal Article20210810This work is concerned with the periodic solution of a doubly degenerate Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Firstly, we define a new associated auxiliary problem. Secondly, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, where this limit point represents a nontrivial nonnegative time-periodic solution of the main studied problem. It is observed that the topological degree theorem technique plays an important role in proving the desired results. Furthermore, this technique can be applied to other similar equations with homogeneous Dirichlet or Neumann boundary conditions.https://ijnaa.semnan.ac.ir/article_5505_38a74da87b97ddb34ded83786807d966.pdf