“…We prove that, the spectrum of the associated differential operator is discrete and the system of roots elements are complete in E-valued weighted L p spaces. Note that, differential-operator equations (DOEs) have been studied extensively by many researchers (see [1,3] , [7,9,11,13,14] , [16][17][18][19][20][21][22][23][24][25][26] and the references therein).…”