As we have noted above, if one compares the results obtained by different reducing schemes for the same variational problem, then the comparison of the types of smooth equivalence for key functions is the main problem. This problem was posed in [138] and partially developed in [138-140]. In this chapter, we use the condition of smooth equivalence for key functions obtained by the Thorn homotopic method (see [10,145, 168, 172]). The main assumption is the possibility of finding smooth deformations of reducing schemes into each other. If the comparison is global, then we use the condition of preservation of the coercivity under the deformation.
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