On a general variational framework for existence and uniqueness in Differential Equations

Pablo Pedregal

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arXiv · 2109.06517

On a general variational framework for existence and uniqueness in Differential Equations

Pablo Pedregal

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Abstract

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some selected examples including initial-value, Cauchy problems for ODEs; non-linear, monotone PDEs; linear and non-linear hyperbolic problems; and steady Navier-Stokes systems.

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Pablo Pedregal. 2021-09-14. On a general variational framework for existence and uniqueness in Differential Equations. https://arxiv.org/abs/2109.06517

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