The integro-differential equation with p-Laplacian operator is widely used in applied mechanics

astrophysics and classical electrology. The boundary value problem of nonlinear differential equations is an important branch of differential equations. Therefore

it is a great theoretical and practical significance to study the boundary value problems of p-Laplacian integro-differential equations. A class of p-Laplacian integro-differential equations with complex boundary conditions on infinite interval is systematically studied. By using the monotone iterative technique

the existence of extremal solutions as well as iterative schemes under the suitable conditions is established. At last

an example is given to demonstrate the use of the main result.