In this paper,we use the Melnikov function method to study a kind of soft Duffing equations(?)+Af((?),x)+x-x<sup>2k+1</sup>=r[M(x,(?))cosωt+N(x,(?))sinωt](k=1,2,3…)and give
This note illustrates the multidimensional dispersion relations that connect the realand imaginary parts of the matrix z(p):where(?)(p)is the boundary value of