Periodic solutions for the 1-dimensional p-Laplacian equation

Abstract

Existence of infinitely many periodic solutions for the 1-dimensional p-Laplacian equation d d t ( | d x d t | p − 2 d x d t ) + 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 − 2 x = + ∞ and f ∈ C ( R × R , R ) is 1-periodic in the time t, and small with respect to g.