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The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives. (English) Zbl 1154.35328
Summary: By setting up appropriate uniform convergence structures, we are able to reformulate the order completion method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.
35G20General theory of nonlinear higher-order PDE
54A20Convergence in general topology
06B30Topological lattices, order topologies
46E05Lattices of continuous, differentiable or analytic functions
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