Firstly, we study the solution of the equation ♢k♢Bku(x)=f(x), where ♢k♢Bk is the composite of the diamond operator and Bessel diamond operator. Finally, we study of the nonlinear equation ♢k♢Bku(x)=f(x,∆k-1□k♢Bk). It was found that the existence of the solution u(x) of such an equation depends on the condition of f and ∆k-1□k♢Bku(x). Moreover, such equation u(x) is related to the elastic wave equation.