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Linked References

1. V. I. Arnold, Lectures on Partial Differential Equations, Springer, Berlin, Germany, 2004.
2. L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1998.
3. S. Kovalevskaia, “Zur Theorie der partiellen differentialgleichung,” Journal für die reine und angewandte Mathematik, vol. 80, pp. 1–32, 1875.
4. E. E. Rosinger, “Global version of the Cauchy-Kovalevskaia theorem for nonlinear PDEs,” Acta Applicandae Mathematicae, vol. 21, no. 3, pp. 331–343, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
5. J.-F. Colombeau, New Generalized Functions and Multiplication of Distributions, vol. 84, North-Holland, Amsterdam, The Netherlands, 1984.
6. M. B. Oberguggenberger and E. E. Rosinger, Solution of Continuous Nonlinear PDEs through Order Completion, vol. 181, North-Holland, Amsterdam, The Netherlands, 1994.
7. R. Anguelov and E. E. Rosinger, “Solving large classes of nonlinear systems of PDEs,” Computers & Mathematics with Applications, vol. 53, no. 3-4, pp. 491–507, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
8. J. H. van der Walt, “The uniform order convergence structure on $ML(X)$,” Quaestiones Mathematicae, vol. 31, no. 1, pp. 55–77, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. J. H. van der Walt, “The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives,” Acta Applicandae Mathematicae, vol. 103, no. 1, pp. 1–17, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. J. H. van der Walt, “The order completion method for systems of nonlinear PDEs revisited,” Acta Applicandae Mathematicae, vol. 106, no. 2, pp. 149–176, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
11. R. Baire, Lecons Sur Les Fonctions Discontinues, Collection Borel, Paris, France, 1905.
12. R. Anguelov, “Dedekind order completion of $C(X)$ by Hausdorff continuous functions,” Quaestiones Mathematicae, vol. 27, no. 2, pp. 153–169, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. R. P. Dilworth, “The normal completion of the lattice of continuous functions,” Transactions of the American Mathematical Society, vol. 68, pp. 427–438, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. J. H. van der Walt, “The completion of uniform convergence spaces and an application to nonlinear PDEs,” Quaestiones Mathematicae, vol. 32, no. 3, pp. 371–395, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. R. Beattie and H.-P. Butzmann, Convergence Structures and Applications to Functional Analysis, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.
16. O. Forster, Analysis 3, Integralrechnung im ℝⁿ mit Anwendungen, vol. 52, Vieweg, Braunschweig, Germany, 1981.
17. L. Hörmander, Linear Partial Differential Operators, Springer, Berlin, Germany, 1976.