Nonlinear L k l operator related to the Bessel-Helmholtz operator and the Bessel Klein-Gordon operator

Abstract

In this article, we study the solution of the nonlinear equation where L kl is defined by and (Δ B + a 2) k and (□ B + b 2) l are defined by (2) and (3) respectively. u is an unknown generalized function and f is a given generalized function. It is found that the existence of the solution u(x) of such an equation depends on the condition of f and L k-1lu(x). Moreover such a solution u(x) is related to the fundamental solution of Bessel-Helmholtz Operator and the Bessel Klein-Gordon Operator.