Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 482467, 20 pages
Research Article

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

Department of Mathematics, Chiangmai University, Chiangmai 50200, Thailand

Received 15 August 2009; Revised 21 November 2009; Accepted 12 January 2010

Academic Editor: Victoria Vampa

Copyright © 2010 Wanchak Satsanit and Amnuay Kananthai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Firstly, we studied the solution of the equation kBku(x)=f(x) where u(x) is an unknown unknown function for x=(x1,x2,,xn)n, f(x) is the generalized function, k is a positive integer. Finally, we have studied the solution of the nonlinear equation kBku(x)=f(x,k1LkΔBkBku(x)). It was found that the existence of the solution u(x) of such an equation depends on the condition of f and k1LkΔBkBku(x). Moreover such solution u(x) is related to the inhomogeneous wave equation depending on the conditions of p, q, and k.