Boundary value problem of the operator ⊕^krelated to the biharmonic operator and the diamond operator

Abstract

© 2018 by the authors. This paper presents an alternative methodology for finding the solution of the boundary value problem (BVP) for the linear partial differential operator. We are particularly interested in the linear operator ⊕k, where ⊕k=kk,kis the biharmonic operator iterated k-times andkis the diamond operator iterated k-times. The solution is built on the Green's identity of the operatorskand ⊕k, in which their derivations are also provided. To illustrate our findings, the example with prescribed boundary conditions is exhibited.