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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.
MSC:
35G20General theory of nonlinear higher-order PDE
54A20Convergence in general topology
06B30Topological lattices, order topologies
46E05Lattices of continuous, differentiable or analytic functions
References:
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