ABSTRACT
This paper is concerned with the existence of sign changing periodic solutions for the Chafee–Infante equation , subject to homogeneous Dirichlet boundary condition. If
, where
is the m-th eigenvalue of the one-dimensional Laplacian, then there exists a periodic solution, whose zero number is less than or equal to
. Specially, if
is independent of t, there exists sign changing stationary solutions. Furthermore, numerical simulations verify our result. In some sense, we generalize the result of Bartsch, Polácik and Quittner [Theorem 1.8] 1 to the case of Chafee–Infante equation.
Acknowledgements
The authors would like to express gratitude to Professor Pavol Quittner and Professor Bendong Lou for their generous help and valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.