Green functions construction of linear differential operators containing parameter

In this thesis, we studied the Green?s function constructions of the linear differential operators. We gave the construction method in the contend of the special definition of the Green?s functions. We explained it by examples. We used the Green?s functions to derive integral equations from parameterized boundary value problems. We showed the existence of the Green?s functions of the parameterized linear differential operators by solving integral equations. We derived the Green?s function construction formulas for the parameterized differential operators. We showed the Green?s function construction methods of linear differential operators using the function. We examined the analytic nature of the parameterized linear differential operators. We showed the Green?s function construction of the parameterized differential operators through the residue formulas of functions of complex variables.