Can there be a general nonlinear PDE theory for existence of solutions

摘要: Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions very large classes nonlinear systems PDEs. This solution method based on Dedekind order completion suitable spaces piece-wise smooth functions Euclidean domains definition respective The can also deal with associated initial and/or boundary value problems. obtained be assimilated usual measurable or even Hausdorff continuous domains. It important note that use does not require any monotonicity condition PDEs involved. One major advantages it eliminates algebra dichotomy "linear versus nonlinear" PDEs, treating both cases equal ease. Furthermore, introduce "monotonous non-monotonous" None known functional analytic methods exhibit such performance, in addition topology, are significantly algebra.