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By means of critical point theory and some analysis methods, the existence of homoclinic solutions for the p-Laplacian system with delay, ddt[|u′(t)|p−2u′(t)]=∇xG(t,u(t),u(t+τ))+∇yG(t−τ,u(t−τ),u(t))+e(t), is investigated. Some new results are obtained. The interesting thing is that the function G(t,x,y) is only required to satisfy a local condition. Furthermore, the results are all explicitly related to the value of delay τ.

Homoclinic solutions for a second-order p-Laplacian functional differential system with local condition