Abstract
We study the general solution of equation , where is the ultrahyperbolic Bessel operator iterated k‐times and is defined by , n is the dimension of , , 2vi = 2βi + 1, βi > −1/2, xi > 0 (i = 1, 2, …, n), f(x) is a given generalized function, u(x) is an unknown generalized function, k is a nonnegative integer, c is a positive constant, and .
Highlights
The n-dimensional ultrahyperbolic operator k iterated k-times is defined by ⎛ ⎞k k ⎝ ∂2 ∂x12 ∂2 ∂x22 ∂2 ∂xp2 − −···− ⎠ q1.1 where p q n, n is the dimension of space Rn, and k is a nonnegative integer
We study the general solution of equation k B,c u x f x, where k B,c is the ultrahyperbolic Bessel operator iterated k-times and is defined by k B,c
The purpose of this study is to find the general solution of equation kB,cu x where k B,c is the ultrahyperbolic
Summary
1.1 where p q n, n is the dimension of space Rn, and k is a nonnegative integer. In 2009, Saglam et al 14 have developed the operator of 1.3 , defined by 1.6 , and it is called the ultrahyperbolic Bessel operator iterated k-times. They have studied the product of the ultrahyperbolic Bessel operator related to elastic waves. Srisombat and Nonlaopon 15 have studied the weak solution of k B,c u x f x, 1.4 where u x and f x are some generalized functions They have developed 1.4 into the form m. 1.6 p q n, n is the dimension of Rn {x : x x1, x2, . . . , xn , x1 > 0, . . . , xn > 0}, Bxi ∂2/∂xi2 2vi/xi ∂/∂xi , 2vi 2βi 1, βi > −1/2, xi > 0 i 1, 2, . . . , n , f x is a given generalized function, u x is an unknown generalized function, k is a nonnegative integer, c is a positive constant, and x ∈ Rn
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