Overstability and resonance
Augustin Fruchard[1]; Reinhard Schäfke[2]
- [1] Université de La Rochelle, Laboratoire de Mathématiques Calcul Asymptotique, Pôle Sciences et Technologie, Avenue Michel Crépeau, 17042 La Rochelle Cedex (France)
- [2] Université Louis Pasteur, Département de Mathématiques, 7 rue René Descartes, 67084 Strasbourg Cedex (France)
Annales de l’institut Fourier (2003)
- Volume: 53, Issue: 1, page 227-264
- ISSN: 0373-0956
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top- R.C. Ackerberg, R.E. O'Malley, Boundary layer Problems Exhibiting Resonance, Studies in Appl. Math. 49 (1970), 277-295 Zbl0198.12901MR269940
- É. BenoÎt, Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation, Bull. Belgian Math. Soc., suppl. `Nonstandard Analysis' (1996), 71-90 Zbl0896.34069MR1409643
- É. BenoÎt, Enlacements de canards, 72 (1990), 63-91, Publications IHES Zbl0737.34018
- É. BenoÎt, J.-L. Callot, F. Diener, M. Diener, Chasse au canard, Collect. Math. 31 (1981), 37-119 Zbl0529.34046
- É. BenoÎt, A. Fruchard, R. Schäfke, G. Wallet, Solutions surstables des équations différentielles complexes lentes-rapides à point tournant, Ann. Fac. Sci. Toulouse VII (1998), 1-32 Zbl0981.34084MR1693589
- É. BenoÎt, A. Fruchard, R. Schäfke, G. Wallet, Overstability : toward a global study, C.R. Acad. Sci. Paris, série I 326 (1998), 873-878 Zbl0922.34048MR1648552
- J.-L. Callot, Bifurcation du portrait de phase pour des équations différentielles linéaires du second ordre ayant pour type l'équation d'Hermite, (1981)
- J.-L. Callot, Champs lents-rapides complexes à une dimension lente, Ann. Sci. École Norm. Sup., 4e série 26 (1993), 149-173 Zbl0769.34005MR1209706
- M. Canalis-Durand, J.-P. Ramis, R. Schäfke, Y. Sibuya, Gevrey solutions of singularly perturbed differential equations, J. reine angew. Math. 518 (2000), 95-129 Zbl0937.34075MR1739408
- L.P. Cook, W. Eckhaus, Resonance in a boundary value problem of singular perturbation type, Studies in Appl. Math. 52 (1973), 129-139 Zbl0264.34070MR342799
- P.P.N. de Groen, The nature of resonance in a singular perturbation problem of turning point type, SIAM J. Math. Anal. 11 (1980), 1-22 Zbl0424.34021MR556493
- F. Diener, Méthode du plan d'observabilité, (1981)
- L. Hörmander, An introduction to complex analysis in several variables, (1966, revised 1973, 1990), Elsevier Science B.V., Amsterdam Zbl0138.06203
- N. Kopell, A geometric approach to boundary layer problems exhibiting resonance, SIAM. J. Appl. Math. 37 (1979), 436-458 Zbl0417.34051MR543963
- W.D. Lakin, Boundary value problems with a turning point, Studies in Appl. Math. 51 (1972), 261-275 Zbl0257.34015MR355236
- C.H. Lin, The sufficiency of Matkowsky-condition in the problem of resonance, Trans. Amer. Math. Soc. 278 (1983), 647-670 Zbl0513.34055MR701516
- B.J. Matkowsky, On boundary layer problems exhibiting resonance, SIAM Review 17 (1975), 82-100 Zbl0276.34055MR358004
- F.W.J. Olver, Sufficient conditions for Ackerberg-O'Malley resonance, SIAM J. Math. Anal. 9 (1978), 328-355 Zbl0375.34034MR470383
- Y. Sibuya, A theorem concerning uniform simplification at a transition point and the problem of resonance, SIAM J. Math. Anal. 12 (1981), 653-668 Zbl0463.34030MR625824
- W. Wasow, Asymptotic expansions for ordinary differential equations, (1965), Interscience, New York Zbl0133.35301MR203188
- W. Wasow, Linear Turning Point Theory, (1985), Springer, New York Zbl0558.34049MR771669