Periodic solutions of some fourth-order nonlinear differential equations

In this paper, using Mawhin’s continuation theorem, we obtain existence results concerning TT-periodic solutions of fourth-order nonlinear differential equations of the type u⁗−pu″−g(t,u)=e(t),u⁗−pu″−g(t,u)=e(t), where p∈Rp∈R, g:R2→Rg:R2→R is continuous, TT-periodic in tt and e:R→Re:R→R is continuous, TT-periodic with mean value zero. Applications are given for the extended Fisher–Kolmogorov and Swift–Hohenberg equations with forcing term.