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Non-differentiable variational principles. (English) Zbl 1077.49033

In this article there are established several variational principles in a nonsmooth framework. These abstract results are obtained by means of a complex operator which generalizes the classical Fréchet differential. The applications are mainly related to the least action principle and the nonlinear Schrödinger equation. In the last part of the paper it is discussed the connection between the non-differentiable principle and the scale relativity theory.

MSC:

49S05 Variational principles of physics
49J40 Variational inequalities
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
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