Variational formulation for every nonlinear problem

Abstract It is shown that for every linear or nonlinear problem, whose solution exists and is unique, one may find many functionals whose minimum is the solution of the problem. They are obtained after a transformation of the given problem into another by the application of an “integrating operator”: this transforms a differential problem into an integro-differential one. The procedure used to obtain such functionals is straightforward and is described in detail. Examples are exhibited and the numerical effectiveness of the method is tested. The variational formulation so obtained contains the classical formulation as a particular case when it exists.

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