Antiperiodic Solutions for a Generalized High-Order (p,q)-Laplacian Neutral Differential System with Delays in the Critical Case

Abstract

By applying the method of coincidence degree, some criteria are established for the existence of antiperiodic solutions for a generalized high-order (p,q)-Laplacian neutral differential system with delays (φp((x(t)-cx(t-τ))(k)))(m-k)=F(t,xθ0(t),xθ1(t)′,…,xθk(t)(k),yϑ0(t),yϑ1(t)′,…,yϑl(t)(l)), (φq((y(t)-dy(t-σ))(l)))(n-l)=G(t,yμ0(t),yμ1(t)′,…,yμl(t)(l),xν0(t),xν1(t)′,…,xνk(t)(k)) in the critical case |c|=|d|=1. The results of this paper are completely new. Finally, an example is employed to illustrate our results.