Works citing   [Publ. RIMS 41 (2005), pp. 757-791]

1. O. Olendski and L. Mikhailovska:
   Curved quantum waveguides in uniform magnetic fields,
   Phys. Rev. B 72, 23, (Dec 2005), art. no. 235314.
   
   
2. E. R. Johnson, M. Levitin and L. Parnovski:
   Existence of eigenvalues of a linear operator pencil in a curved waveguide - Localized shelf waves on a curved coast,
   SIAM J. Math. Anal. 37 (2006), no. 5, 1465-1481.
   
   
3. S. Kondej and I. Veselic:
   Spectral gap of segments of periodic waveguides,
   Lett. Math. Phys.79 (Jan 2007), no. 1, 95-98.
   
   
4. C. Lin and Z. Lu:
   Existence of bound states for layers built over hypersurfaces in $R^{n+1}$,
   J. Funct. Anal. 244 (2007), 1-25.
   
   
5. O. Olendski and L. Mikhailovska:
   A straight quantum wave guide with mixed Dirichlet and Neumann boundary conditions in uniform magnetic fields,
   J. Phys. A: Math. Theor. 40 (2007), 4609-4633.
   
   
6. A. B. Mikhailova, B. S. Pavlov and L. V. Prokhorov:
   Intermediate Hamiltonian via Glazman's splitting and analytic perturbation for meromorphic matrix-functions,
   Math. Nachr. 280 (2007), 1376-1416.
   
   
7. J. Postnova and R. V. Craster:
   Trapped modes in elastic plates, ocean and quantum waveguides,
   Wave Motion 45 (2008), 565-579.
   
   
8. F. Lledo and O. Post:
   Existence of spectral gaps, covering manifolds and residually finite groups,
   Rev. Math. Phys. 20 (2008), 199-231.
   
   
9. O. Olendski and L. Mikhailovska:
   Analytical and numerical study of a curved planar waveguide with combined Dirichlet and Neumann boundary conditions in a uniform magnetic field,
   Phys. Rev. B 77 (2008), Art. No. 174405.
   
   
10. M. Levitin and M. Marletta:
    A simple method of calculating eigenvalues and resonances in domains with infinite regular ends,
    Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 1043-1065.
    
    
11. M. D. Malykh:
    On the emptiness criteria for the discrete spectrum of the Dirichlet problem for the equation Delta nu plus lambda nu=0,
    Comp. Math. Math. Phys. 49 (2009), 279-283.
    
    
12. H. Najar, S. Ben Hariz and M. Ben Salah:
    On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window,
    Math. Phys. Anal. Geom. 13 (2010), 19-28.
    
    
13. O. Olendski and L. Mikhailovska:
    Theory of a curved planar waveguide with Robin boundary conditions,
    Phys. Rev. E 81 (2010), Art. No. 036606.
    
    
14. H. Najar and O. Olendski:
    Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs,
    J. Phys. A: Math. Theor. 44 (2011), Art. No. 305304.
    
    
15. D. Borisov and G. Cardone:
    Planar waveguide with "twisted" boundary conditions: Discrete spectrum,
    J. Math. Phys. 52, 12, (dec 2011), art. no. 123513.
    
    
16. G. Kaoullas and E. R. Johnson:
    Isobath variation and trapping of continental shelf waves,
    J. Fluid Mech. 700 (2012), 283-303.
    
    
17. N. Charalambous and Z. Lu:
    On the spectrum of the Laplacian,
    Math. Ann. 359 (2014), 211-238.
    
    
18. P. Freitas and P. Siegl:
    Spectra of graphene nanoribbons with armchair and zigzag boundary conditions,
    Rev. Math. Phys. 26 (2014), 1450018.
    
    
19. N. Raymond:
    Breaking a magnetic zero locus: Asymptotic analysis,
    Math. Mod. Meth. Appl. S. 24 (2014), 2785-2817.
    
    
20. V. Bonnaille-Noel and N. Raymond:
    Breaking a magnetic zero locus: model operators and numerical approach,
    Z. Angew. Math. Phys. 95 (2015), 120-139.
    
    
21. M. Bures and P. Siegl:
    Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law,
    Ann. Phys. 354 (2015), 316-327.
    
    
22. G. P. Leonardi:
    An Overview on the Cheeger Problem,
    Edited by: Pratelli, A; Leugering, G Conference: workshop on Trends in shape optimization Location: Erlangen, GERMANY Date: 2013.
    Book Series: International Series of Numerical Mathematics 166 (2015), 117-139.
    
    
23. H. Najar and M. Raissi:
    A quantum waveguide with Aharonov-Bohm magnetic field,
    Math. Meth. Appl. Sci. 39 (2016), 92-103.
    
    
24. S. Jimbo and K. Kurata:
    Asymptotic Behavior of Eigenvalues of the Laplacian on a Thin Domain under the Mixed Boundary Condition,
    Indiana Univ. Math. J. 65 (2016), 867-898.
    
    
25. G. P. Leonardi and A. Pratelli:
    On the Cheeger sets in strips and non-convex domains,
    Calc. Var. Partial Differ. Equ. 55 (2016), 867-898.
    
    
26. A. Pratelli and G. Saracco:
    On the generalized Cheeger problem and an application to 2d strips,
    Rev. Mat. Iberoamericana 33 (2017), 219-237.
    
    
27. C. R. De Oliveira and A. A. Verri:
    Mild singular potentials as effective Laplacians in narrow strips,
    Math. Scand. 120 (2017), 145-160.
    
    
28. J. Royer:
    Local energy decay and diffusive phenomenon in a dissipative wave guide,
    J. Spectr. Theory 8 (2018), 769-841.
    
    
29. C. R. Mamani and A. A. Verri:
    Influence Of Bounded States In The Neumann Laplacian In A Thin Waveguide,
    Rocky Mt. J. Math. 48 (2018), 1993-2021.
    
    
30. M. Malloug and J. Royer:
    Energy Decay In A Wave Guide With Dissipation At Infinity,
    ESAIM: COCV 24 (2018), 519-549.
    
    
31. A. F. Rossini:
    On the spectrum of Robin Laplacian in a planar waveguide,
    Czechoslovak Math. J. 69 (2019), 485-501.
    
    
32. M. Karuhanga:
    On the discrete spectrum of Schrodinger operators with Ahlfors regular potentials in a strip,
    J. Math. Anal. Appl. 475 (2019), 918-938.
    
    
33. S. Kim:
    Application of a complete radiation boundary condition for the Helmholtz equation in locally perturbed waveguides,
    J. Comput. Appl. Math. 367 (2020) UNSP 112458.
    
    
34. C. de Oliveira and A. A. Verri:
    On the Neumann Laplacian in nonuniformly collapsing strips,
    Commun. Contemp. Math. 22 (2020) 1950021.