Periodic solutions for p-Laplacian neutral Liénard equation with a sign-variable coefficient

Using Luʹs continuation theorem, the extension one of Manásevich–Mawhin, we study the existence of periodic solutions for p-Laplacian neutral Liénard equation of the form ( ϕ p ( x ( t ) - cx ( t - σ ) ) ′ ) ′ + f ( x ( t ) ) x ′ ( t ) + β ( t ) g ( x ( t - τ ( t ) ) = e ( t ) . It is meaningful that the coefficient β ( t ) ahead of the nonlinear term g ( x ( t - τ ( t ) ) is allowed to change sign in this paper, which could be achieved infrequently in corresponding papers.