Introduction to the theory of singular perturbations
IIIe rencontre de géométrie du Schnepfenried Volume 2 - 10-15 mai 1982, Astérisque no. 109-110  (1983), p. 67-100
@incollection{AST_1983__109-110__67_0,
     author = {de Jager, E. M.},
     title = {Introduction to the theory of singular perturbations},
     booktitle = {IIIe rencontre de g\'eom\'etrie du Schnepfenried Volume 2 - 10-15 mai 1982},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {109-110},
     year = {1983},
     pages = {67-100},
     zbl = {0531.34044},
     mrnumber = {753144},
     language = {en},
     url = {http://www.numdam.org/item/AST_1983__109-110__67_0}
}
de Jager, E. M. Introduction to the theory of singular perturbations, in IIIe rencontre de géométrie du Schnepfenried Volume 2 - 10-15 mai 1982, Astérisque, no. 109-110 (1983), pp. 67-100. http://www.numdam.org/item/AST_1983__109-110__67_0/

1. R. C. Ackerberg and R. E. O'Malley, Boundary layer problems exhibiting resonance, Stud. Appl. Math. 49, pp. 277-295, 1970. | Article | MR 269940 | Zbl 0198.12901

2. J. G. Besjes, Singular perturbation problems for partial differential equations, Thesis Technical University Delft, the Netherlands, 1973.

3. J. L. Callot, F. Diener, and M. Diener, Chasse au Canard, Series de math. pures et appliquées, IRMA, Strasbourg, 1977. | Zbl 0529.34046

4. P. Cook and W. Eckhaus, Resonance in a boundary value problem of singular perturbation type, Stud. Appl. Math. 52, pp. 129-139, 1973. | Article | MR 342799 | Zbl 0264.34070

5. A. A. Dorodnicyn, Asymptotic solution of the van der Pol equation, A.M.S. Transl. series 1, 4, pp. 1-23, 1962.

6. W. Eckhaus, Asymptotic analysis of singular perturbations. Studies in Mathematics and its Applications, North Holland, 1979. | MR 553107 | Zbl 0421.34057

7. W. Eckhaus and E.M. De Jager Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Arch. Rat. Mech. Anal. 23, pp. 26-86, 1966. | Article | MR 206464 | Zbl 0151.15101

8. P. C. Fife, Semi-linear elliptic boundary value problems with small parameter. Arch. Rat. Mech. Anal. 52, pp. 205-232, 1973. | Article | MR 374665 | Zbl 0268.35007

9. R. Geel, Singular perturbations of hyperbolic type, Mathematical Centre Tract, Math. Centre, 98, Amsterdam, 1979. | MR 527627 | Zbl 0498.35001

10. R. Geel and E.M. De Jager, Hyperbolic singular perturbations of non-linear first order differential equations ; Differential Equations and Applications, Proceedings 3rd Scheveningen Conf. on Diff. Eqs. W. Eckhaus and E.M. de Jager editors, North Holland Publ. Cy, 1978. | MR 516170 | Zbl 0408.35011

11. J. Genet and M. Madaune, Perturbations singulières pour une classe de problèmes hyperboliques non linéaires ; Proceedings of the Conference on Singular Perturbations and Boundary Layer Theory, Lyon 1976, Lecture Notes in Math., vol. 594, Springer, 1977. | Article | MR 486952 | Zbl 0358.35007

12. J. Grasman, On the birth of boundary layers, Mathematical Centre Tract, vol. 36, Math. Centre, Amsterdam, 1971. | MR 462165 | Zbl 0228.35012

13. J. Grasman and B. J. Matkovsky A variational approach to singularly perturbed, boundary value problems for ordinary and partial differential equations with turning points, SIAM J. Appl. Math., 32, no. 3, 1977. | Article | MR 430444 | Zbl 0392.34038

14. P. P. N De Groen, Spectral properties of second order singularly perturbed boundary value problems with turning points, J. Math. Anal. Appl. 57, pp. 119-149, 1977. | Article | MR 440112 | Zbl 0345.34045

15. J. Haag, Étude asymptotique des oscillations de relaxation, Ann. Sci. Ecole Norm. Sup., 60, 1943. | MR 14538 | Zbl 0061.19107

16. J. Haag, Exemples concrets d'étude asymptotiques d'oscillations de relaxation, Ann. Sci. Ecole Norm. Sup., 61, 1944. | MR 14539 | Zbl 0061.19108

17. W. A. Harris, Singular perturbations of two point boundary problems for systems of ordinary differential equations, Arch. Rat. Mech. An. 5, pp. 212-225, 1960. | Article | MR 117412 | Zbl 0098.05801

18. W. A. Harris, Singular perturbations of two point boundary problems. J. Math.Mech. 11, pp. 371-382, 1962. | MR 141852 | Zbl 0121.07202

19. A. Van Harten, Singularly perturbed non-linear 2nd order elliptic boundary value problems, Thesis, University of Utrecht, 1975.

20. D. Huet, Phénomènes de perturbation singulière dans les problèmes aux limites, Ann. Inst. Fourier, Grenoble, 10, 1960. | Article | MR 118968 | Zbl 0128.32904

21. E.M. De Jager, Singular perturbations of hyperbolic type, Nieuw Archief voor Wiskunde, 23 (3), pp. 145-172, 1975. | MR 377242 | Zbl 0304.35007

22. E.M. De Jager and R. Geel Singular perturbations of hyperbolic type, Analytical and Numerical Approaches to Asymptotic Problems in Analysis, editors O. Axelson, L.S. Frank, A.v.d. Sluis, North Holl. Publ. Cy, Amsterdam 1981. | MR 605499 | Zbl 0457.35008

23. E. M. De Jager, Singuläre Störungen von nicht linearen Operatoren, ZAMM, 60, 1980. | MR 607474 | Zbl 0452.34048

24. E. M. De Jager and P. Wilders The Korteweg-de Vries equation as a singular perturbation problem, University of Amsterdam, Dept. of Mathematics, Rep. 82-07, 1982.

25. P. D. Lax and C. D. Levermore The zero dispersion limit for the Korteweg-de Vries equation, Proc. Natl. Ac. Sc. U.S.A., 76, no. 8, Mathematics, pp. 3602-3606, August 1979. | Article | MR 540258 | Zbl 0411.35081

26. J. L. Lions, Perturbations singulières dans les problèmes aux limites et en controle optimal, Lecture Notes in Mathematics, 323, Springer 1973. | MR 600331 | Zbl 0268.49001

27. R. Lutz and M. Goze, Non-standard analysis, a practical guide with applications, Lecture Notes in Mathematics, 881, Springer, 1981. | MR 643624 | Zbl 0506.03021

28. R. Lutz and T. Sari, Sur le comportement asymptotique des solutions dans un problème aux limites non linéaire, CRAS, 292, Série I, pp. 925-928, 1981. | MR 625369 | Zbl 0464.34039

29. M. Madaune, Perturbations singulières de type hyperbolique-hyperbolique non linéaire, Publ. Math., Université de Pau, 1977.

30. M. Madaune, Thèse Université de Pau, 1981.

31. A. H. Nayfeh, Perturbation methods, Wiley, 1973. | MR 404788

32. O. A. Oleinik, Construction of a generalized solution of the Cauchy problem for a quasi linear equation of first order by the introduction of vanishing viscosity, A.M.S. Transl. Series 2, 33, 1963. | Zbl 0131.09101

33. R. E. O'Malley Singular perturbations of boundary value problems for linear ordinary differential equations involving two parameters, J. Math. Anal. Appl., 19, pp. 291-308, 1967. | Article | MR 213663 | Zbl 0166.08001

34. R. E. O'Malley, Boundary value problems for linear systems of ordinary differential equations involving many small parameters, J. Math. Mech, 18, pp. 835-853, 1969. | MR 251324 | Zbl 0177.11901

35. M. H. Protter and H. F. Weinberger Maximum principles in differential equations, Prentice Hall, 1967. | MR 219861 | Zbl 0153.13602

36. A. Robinson, Non-standard analysis, Studies in Logic, North Holland Publ. Cy, Amsterdam, 1966. | MR 205854 | Zbl 0151.00803

37. N. Rouché and J. Mawhin Equations différentielles ordinaires, t. 1, Masson et Cie, 1973. | MR 481181 | Zbl 0289.34001

38. T. Sari, Sur le comportement asyomptotique des solutions dans un problème aux limites semi-linéaire, CRAS, 292, Série I, pp. 867-870, 1981. | MR 623518 | Zbl 0464.34038

39. A. Troesch, Etude qualitative de systèmes differentiels: une approche basée sur l'analyse non standard, Thèse Université Louis Pasteur Strasbourg, IRMA 1981.

40. A. Troesch and E. Urlacher Analyse non standard et equations de van der Pol ; Perturbations singulières et analyse non standard, Series de Mathematiques Pures et Appliquées, IRMA, Strasbourg 1976-1977. | MR 520773

41. E. Urlacher, Oscillation de relaxation et analyse non standard, Thèse Université Louis Pasteur, Strasbourg, IRMA 1981.

42. M. I. Višik and L. A. Lyusternik Regular degeneration and boundary layer for linear, differential equations with a small parameter, AMS Transl., Series 2, 20, pp. 239-364, 1962. | MR 136861 | Zbl 0122.32402

43. W. Wasow, The capriciousness of singular perturbations, Nieuw Archief voor Wiskunde, 18(3), pp. 190-210, 1970. | MR 277848 | Zbl 0204.40603

44. W. Wasow, On the asymptotic solution of boundary value problems for ordinary differential equations containing a parameter, J. Math Phys., 32, pp. 173-183, 1944. | Article | MR 10907 | Zbl 0061.18202

45. W. Eckhaus and E. M. De Jager Theory and Applications of singular perturbations Proceedings Oberwolfach 1981, Lecture Notes in Mathematics, 942, Springer, 1982. | MR 679341 | Zbl 0478.00011

46. C. Bardos, D. Brezis and M. Brezis Perturbations singulières et prolongements maximaux d'opérateurs positifs, Arch. Rationel Mech. Anal. 53, pp. 69-100, 1973. | Article | MR 348247 | Zbl 0281.47028

47. A. Bensoussan, J.-L. Lions, G. Papanicolaou Asymptotic Analysis for periodic structures, North Holland Publ. Cy, Amsterdam, 1978. | MR 503330 | Zbl 0404.35001

48. N. Kruckov First order quasilinear equations in several space variables, Math. USSR Sbornik, vol. 10, n° 2, pp. 217-243, 1978. | Article | Zbl 0215.16203