Positive periodic solution for high-order p -Laplacian neutral differential equation with singularity

摘要

In this paper, we consider the following high-order p-Laplacian neutral differential equation with singularity: ( φ p ( x ( t ) − c x ( t − τ ) ) ( n ) ) ( m ) + f ( x ( t ) ) x ′ ( t ) + g ( t , x ( t − σ ) ) = e ( t ) . $$ igl(arphi_{p}igl(x(t)-cx(t-au)igr)^{(n)} igr)^{(m)}+figl(x(t)igr)x'(t)+gigl(t,x(t-sigma) igr)=e(t). $$ By applications of coincidence degree theory and some analysis techniques, sufficient conditions for the existence of positive periodic solutions are established.