S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N -body Schrödinger operators, volume 29 of Mathematical Notes, 1982.
DOI : 10.1515/9781400853076

A. Bernoff and P. Sternberg, Onset of superconductivity in decreasing fields for general domains, Journal of Mathematical Physics, vol.39, issue.3, pp.1272-1284, 1998.
DOI : 10.1063/1.532379

V. Bonnaillie-no¨elno¨ and . No¨el, Harmonic oscillators with Neumann condition on the halfline, Commun. Pure Appl. Anal. To appear, 2011.

B. Chenaud, P. Duclos, P. Freitas, and D. Krej?i?´ikkrej?krej?ikrej?i?krej?i?krej?i?´krej?i?´ik, Geometrically induced discrete spectrum in curved tubes, Differential Geometry and its Applications, vol.23, issue.2, pp.95-105, 2005.
DOI : 10.1016/j.difgeo.2005.05.001

H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators with application to quantum mechanics and global geometry. Texts and Monographs in Physics, 1987.

M. Dauge and B. Helffer, Eigenvalues Variation. I., Journal of Differential Equations, vol.104, issue.2, pp.243-262, 1993.
DOI : 10.1006/jdeq.1993.1071

P. Duclos and P. Exner, CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS, Reviews in Mathematical Physics, vol.07, issue.01, pp.73-102, 1995.
DOI : 10.1142/S0129055X95000062

S. Fournais and B. Helffer, Spectral methods in surface superconductivity, Progress in Nonlinear Differential Equations and their Applications, 2010.
DOI : 10.1007/978-0-8176-4797-1

B. Helffer, Semi-classical analysis for the Schrödinger operator and applications, volume 1336 of Lecture Notes in Mathematics, 1988.

B. Helffer and A. Morame, Magnetic bottles for the Neumann problem: The case of dimension 3, Proceedings Mathematical Sciences, vol.210, issue.2, pp.71-84, 2000.
DOI : 10.1007/BF02829641

B. Helffer, J. Sj¨ostrandsj¨, and . Sj¨ostrand, Multiple wells in the semi-classical limit I, Communications in Partial Differential Equations, vol.52, issue.2, pp.337-408, 1984.
DOI : 10.1080/03605308408820335

M. E. Ismail and R. Zhang, On the Hellmann-Feynman theorem and the variation of zeros of certain special functions, Advances in Applied Mathematics, vol.9, issue.4, pp.439-446, 1988.
DOI : 10.1016/0196-8858(88)90022-X

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, 1995.
DOI : 10.1007/978-3-662-12678-3

K. Lu and X. Pan, Surface Nucleation of Superconductivity in 3-Dimensions, Journal of Differential Equations, vol.168, issue.2, pp.386-452, 1998.
DOI : 10.1006/jdeq.2000.3892

A. Martinez, Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer, Ann. Inst. H. Poincaré Phys. Théor, vol.50, issue.3, pp.239-257, 1989.
DOI : 10.5802/jedp.354

A. Morame and F. Truc, Remarks on the spectrum of the Neumann problem with magnetic field in the half-space, Journal of Mathematical Physics, vol.46, issue.1, p.12105, 2005.
DOI : 10.1063/1.1827922

URL : https://hal.archives-ouvertes.fr/hal-00381535

A. Persson, Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schr??dinger Operator., MATHEMATICA SCANDINAVICA, vol.8, pp.143-153, 1960.
DOI : 10.7146/math.scand.a-10602

N. Raymond, Sharp Asymptotics for the Neumann Laplacian with Variable Magnetic Field: Case of Dimension 2, Annales Henri Poincar??, vol.10, issue.1, pp.95-122, 2009.
DOI : 10.1007/s00023-009-0405-0

N. Raymond, On the semi-classical 3D Neumann Laplacian with variable magnetic field, Asymptotic Analysis, vol.68, issue.12, pp.1-40, 2010.

M. R. and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, 1978.

M. Schatzman, Analyse numérique. InterEditions Cours et exercices pour la licence. [Course and exercises for the bachelor's degree], 1991.

M. I. Vi?ikvi?vi?ik and L. A. Ljusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Amer. Math. Soc. Transl, issue.2, pp.20-239, 1962.