(untitled) (Analysis in Theory and Applications, 2014)
In this paper, we study an ODE of the formb_0 u^(4) + b_1 u'' + b_2 u + b_3 u^3 + b_4 u^5 = 0, ' = dd z, which includes, as a special case, the stationary case of the cubic-quintic Swift-Hohenberg equation. Based on Nevanlinna theory and Painlevé analysis, we first show that all its meromorphic solutions are elliptic or degenerate elliptic. Then we obtain them all explicitly by the method introduced in [7].