Solvability of the resonant 1-dimensional periodic p-Laplacian equations

In this paper we study the existence of 2π-periodic solutions of − ( | x ′ | p − 2 x ′ ) ′ = λ | x | p − 2 x + f ( t ) , x ∈ R where p > 1 , λ is an eigenvalue of the corresponding homogeneous equation, f is a 2π-periodic function. Some existence results are proved via the Morse theory.