Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric
Stuart, Charles A. ; Zhou, Huan-Song
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001), p. 69-96 / Harvested from Numdam
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Publié le : 2001-01-01
@article{AIHPC_2001__18_1_69_0,
     author = {Stuart, Charles A. and Zhou, Huan-Song},
     title = {Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {18},
     year = {2001},
     pages = {69-96},
     mrnumber = {1810271},
     zbl = {0992.78006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2001__18_1_69_0}
}

Stuart, Charles A.; Zhou, Huan-Song. Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) pp. 69-96. http://gdmltest.u-ga.fr/item/AIHPC_2001__18_1_69_0/

1 Bartolo P, Benci V, Fortunato D, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal. TMA Vol. 7 (9) (1983) 981-1012. | MR 713209 | Zbl 0522.58012

2 Chen Y, TE and TM families of self-trapped beams, IEEE J. Quantum Electronics Vol. 27 (1991) 1236-1241.

3 Chen Y, Snyder A.W, TM-type self-guided beams with circular cross-section, Electr. Lett. Vol. 27 (1991) 564-566.

4 Jeanjean L, On the existence of bounded Palais-Smale sequences and application to a Landesman-Lazer type problem, Proc. Royal Soc. Edinburgh, Ser. A Vol. 129A (1999) 787-809. | Zbl 0935.35044

5 John O, Stuart C.A, Guidance properties of a cylindrical defocusing waveguide, Comm. Math. Univ. Carolinae Vol. 35 (1994) 653-673. | MR 1321236 | Zbl 0819.35137

6 Lebedev N.N, Special Functions and their Applications, Dover, 1972. | MR 350075 | Zbl 0271.33001

7 Rabinowitz P.H, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc, Providence, RI, 1986. | MR 845785 | Zbl 0609.58002

8 Ruppen H.-J, Multiple cylindrical TE-Modes for a homogeneous self-focusing dielectric, Nonlinear World Vol. 2 (1995) 387-418. | MR 1360868 | Zbl 0833.34038

9 Ruppen H.-J, Multiple cylindrical TM-Modes in a homogeneous self-focusing dielectric, J. Differential Equations Vol. 201 (1997) 112-123. | Zbl 0898.34017

10 Showalter R.E, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs (AMS), Vol. 49, 1997. | MR 1422252 | Zbl 0870.35004

11 Stuart C.A, Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rat. Mech. Anal. Vol. 113 (1991) 65-96. | MR 1079182 | Zbl 0745.35044

12 Stuart C.A, Cylindrical TM-modes in a homogeneous self-focusing dielectric, Math. Models Methods Appl. Sci. Vol. 6 (1996) 977-1008. | MR 1419240 | Zbl 0934.35190

13 Stuart C.A, Magnetic field wave equations for TM-modes in nonlinear optical waveguides, in: Caristi , Mitidieri (Eds.), Reaction Diffusion Systems, Marcel Dekker, 1997. | MR 1472530 | Zbl 0894.35111

14 Stuart C.A, Zhou H.S, A variational problem related to self-trapping of an electromagnetic field, Math. Methods Appl. Sci. Vol. 19 (1996) 1397-1407. | MR 1414401 | Zbl 0862.35123