Periodic solutions for the 1-dimensional p-Laplacian equation

Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equationddt(|dxdt|p−2dxdt)+g(x)=f(t,x) is proved by means of the Poincaré–Birkhoff fixed point theorem, where g∈C(R,R)g∈C(R,R) and is p-sublinear at the origin in the senselim|x|→0g(x)|x|p−2x=+∞ and f∈C(R×R,R)f∈C(R×R,R) is 1-periodic in the time t, and small with respect to g.