Periodic solutions for the 1-dimensional p-Laplacian equation

Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equation d dt dx dt p−2 dx dt +g(x) = f (t,x) is proved by means of the Poincaré–Birkhoff fixed point theorem, where g ∈ C(R,R) and is p-sublinear at the origin in the sense lim |x|→0 g(x) |x|p−2x =+∞ and f ∈ C(R ×R,R) is 1-periodic in the time t , and small with respect to g. © 2006 Elsevier Inc. All rights reserved