On the Solution n-Dimensional of the Product ⊗k Operator and Diamond Bessel Operator

Abstract EN

Firstly, we studied the solution of the equation ⊗k◊Bku(x)=f(x) where u(x) is an unknown unknown function for x=(x1,x2,…,xn)∈ℝn, f(x) is the generalized function, k is a positive integer.

Finally, we have studied the solution of the nonlinear equation ⊗k◊Bku(x)=f(x,□k−1LkΔBk□Bku(x)).

It was found that the existence of the solution u(x) of such an equation depends on the condition of f and □k−1LkΔBk□Bku(x).

Moreover such solution u(x) is related to the inhomogeneous wave equation depending on the conditions of p, q, and k.