Abstract: A class of p-Laplace equation with a nonsymmetric term on a bounded domain is studied.By using the large Morse index of the corresponding Laplace equation,we give a growth estimate about the series of min-max values of associated functional for the problem.The estimate is better than the given result in some range.It is shown that the problem possesses infinitely many weak solutions.

Key words: p-Laplace equation, large Morse index, non-symmetric perturbation；infinitely many solutions