On the solution n -dimensional of the product k operator and diamond bessel operator

Abstract

Firstly, we studied the solution of the equation ⊗k◇Bku (x) = f (x) where u (x) is an unknown unknown function for x = (x 1, x 2,⋯,xn) n, f (x) is the generalized function, k is a positive integer. Finally, we have studied the solution of the nonlinear equation ⊗k B ◇u(x) = f(x,k- 1LkΔBkBku (x)). It was found that the existence of the solution u (x) of such an equation depends on the condition of f andk-1LkΔBkBku(x). Moreover such solution u (x) is related to the inhomogeneous wave equation depending on the conditions of p, q, and k. Copyright © 2010 W. Satsanit and A. Kananthai.