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

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable many situations of existence in Differential Equations. This unifying feature is quite appealing and motivated our analysis. We show its potentiality with some selected examples including initial-value, Cauchy problems for ODEs; non-linear, monotone PDEs; linear non-linear hyperbolic problems; steady Navier–Stokes systems. Though paper has structure survey, would like explore future how this perspective could help advancing new PDEs.