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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: $$ bigl(varphi_{p}bigl(x(t)-c(t)x(t-sigma)bigr)^{(n)} bigr)^{(m)}+fbigl(t,xu0027(t)bigr)+gbigl(t,x(t)bigr)=e(t). $$Our proof is based on Mawhin’s continuation theory.

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