The compound equation related to the Bessel-Helmholtz equation and the Bessel-Klein-Gordon equation

Abstract

In this paper we study the compound equation where x = (x1, x2, . . . , xn) ∈ ℝn+ = {x ∈ ℝn | xi > 0}, a and b are nonzero constants. u(x) is unknown function and f(x) is a given distribution. (δB + a2)i is the Bessel-Helmholtz operator iterated i-times and ({combining square below}B + b2)j is the Bessel-Klein-Gordon operator iterated j-times. The existence and the uniqueness solution of (1) is proven. © 2013 Chalermpon Bunpog.