The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition

Document Type : Research Paper


1 Department of Mathematics, College of education for pure science, Tikrit University, Iraq

2 Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq

3 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.


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Volume 13, Issue 1
March 2022
Pages 397-408
  • Receive Date: 10 August 2021
  • Revise Date: 03 September 2021
  • Accept Date: 26 September 2021
  • First Publish Date: 26 September 2021