Abstract: We considered the existence of weak solutions to  elliptic coupled systems with p-Laplace operators and Hardy type singular terms in the whole space R^N. New criteria for the existence of at least one and at least two weak solutions were established by using  variational methods combined with  critical point theorems when the sign-changing nonlinearities satisfied suitable hypotheses.

Key words: p-Laplace operator, elliptic coupled system, Hardy singular term, whole space R^N, weak solution