Boundary Value Problem of the Operator ⊕k Related to the Biharmonic Operator and the Diamond Operator

Abstract

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=♡k♢k, ♡k is the biharmonic operator iterated k-times and ♢k is the diamond operator iterated k-times. The solution is built on the Green’s identity of the operators ♡k and ⊕k, in which their derivations are also provided. To illustrate our findings, the example with prescribed boundary conditions is exhibited.

Keywords

• boundary value problem
• Green’s identity
• Green’s function
• tempered distribution