Positive periodic solution for higher-order p-Laplacian neutral singular Rayleigh equation with variable coefficient

Abstract In this paper, we consider the existence of a positive periodic solution for the following kind of high-order p-Laplacian neutral singular Rayleigh equation with variable coefficient: ( φ p ( x ( t ) − c ( t ) x ( t − σ ) ) ( n ) ) ( m ) + f ( t , x ′ ( t ) ) + g ( t , x ( t ) ) = e ( t ) . $$ \bigl(\varphi_{p}\bigl(x(t)-c(t)x(t-\sigma)\bigr)^{(n)} \bigr)^{(m)}+f\bigl(t,x'(t)\bigr)+g\bigl(t,x(t)\bigr)=e(t). $$ Our proof is based on Mawhin’s continuation theory