On the solution \(n\)-dimensional of the composite \(\diamond^k\) operator and \(\diamond^k_B\) operator (Q1954432)

Summary: We study the solution of the equation \(\diamond^k \diamond^k_B u(x) = f(x)\), where \(\diamond^k \diamond^k_B\) is the composite of the diamond operator and Bessel diamond operator. Furthermore, we study of the nonlinear equation \(\diamond^k \diamond^k_B u(x) = f(x, \triangle^{k-1} \square^k \diamond^k_B)\). It was found that the existence of the solution \(u(x)\) of such an equation depends on the condition of \(f\) and \(\triangle^{k-1} \square^k \diamond^k_B u(x)\). Moreover, such equation \(u(x)\) is related to the elastic wave equation.