Document Type : Research Paper
Department of Mathematics, College of education for pure science, Tikrit University.
Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Department of Mathematics, College of Education, Al- Hamdaniya University, Mosul, Iraq
This 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.