Abstract: The variational principle (VP) of classical type (excluding the Blot's VP, the Gurtin'sVP, the least square VP & various constrained VP, in which some unknown variables are frozenduring the variation operation) for the entitled problem is extremely difficult to establish, so that upto now all VP for this problem, to more or less degree, are constrained VP with the only exception ofthe Grutin's VP. However, the Gurtin's VP posesses the following two essential short-comings: 1) itis confined only to linear di...