The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator - Niyom S. (2017)
In this paper, we study the solution of nonlinear equation Δ k B (Δ B + m 2 ) k u(x) = f(x,Δ k-1 B (Δ B + m 2 ) k u(x)) where the operator Δ k B is the Bessel Laplace operator iterated k-times defined by Δ k B = (B x1 + B x2 + · · · + B xn ) k n is the dimension of the space R + n , x = (x 1 , x 2 ,..., x n ) E R + n , k is a positive integer, u(x) is an unknown and f is a given function. It is found that the existence of the solution u(x) of such equation depending on the condition of f and Δ k-1 B (Δ B +m 2 ) k u(x). Moreover such solution u(x) related to the nonhomogeneous Bessel biharmonic equation depend on the conditions of k.