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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:
49S05Variational principles of physics
49J40Variational methods including variational inequalities
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
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References:
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