文摘
In this paper, the authors prove an analogue of Gibbons’ conjecture for the extended fourth order Allen-Cahn equation in ℝN, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.