American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 403-409. doi: 10.3934/proc.2005.2005.403

A bound for ratios of eigenvalues of Schrodinger operators on the real line

Miklós Horváth 1, and  Márton Kiss 1,

1. 

Department of Mathematical Analysis, Budapest University of Technology and Economics, H 1111 Budapest, Müegyetem rkp. 3-9, Hungary, Hungary

Received  September 2004 Revised  May 2005 Published  September 2005

We give upper estimates of ratios of eigenvalues of Schrödinger operators with nonnegative single-well potentials tending to infinity for large $|x|$, corresponding to previous estimates on a finite interval.
Keywords: Schrodinger operator, eigenvalues..
Mathematics Subject Classification: Primary 34L15, 34B2.
Citation: Miklós Horváth, Márton Kiss. A bound for ratios of eigenvalues of Schrodinger operators on the real line. Conference Publications, 2005, 2005 (Special) : 403-409. doi: 10.3934/proc.2005.2005.403
[1]

Lassi Päivärinta, Valery Serov. Recovery of jumps and singularities in the multidimensional Schrodinger operator from limited data. Inverse Problems & Imaging, 2007, 1 (3) : 525-535. doi: 10.3934/ipi.2007.1.525
[2]

Nakao Hayashi, Pavel I. Naumkin. Modified wave operator for Schrodinger type equations with subcritical dissipative nonlinearities. Inverse Problems & Imaging, 2007, 1 (2) : 391-398. doi: 10.3934/ipi.2007.1.391
[3]

A. M. Micheletti, Angela Pistoia. Multiple eigenvalues of the Laplace-Beltrami operator and deformation of the Riemannian metric. Discrete & Continuous Dynamical Systems, 1998, 4 (4) : 709-720. doi: 10.3934/dcds.1998.4.709
[4]

Yoshitsugu Kabeya. Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3529-3559. doi: 10.3934/dcds.2020040
[5]

Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli. Smoothing-Strichartz estimates for the Schrodinger equation with small magnetic potential. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 771-786. doi: 10.3934/dcds.2007.17.771
[6]

Marilena N. Poulou, Nikolaos M. Stavrakakis. Global attractor for a Klein-Gordon-Schrodinger type system. Conference Publications, 2007, 2007 (Special) : 844-854. doi: 10.3934/proc.2007.2007.844
[7]

Anatoli Babin, Alexander Figotin. Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1685-1718. doi: 10.3934/cpaa.2014.13.1685
[8]

Maike Schulte, Anton Arnold. Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme. Kinetic & Related Models, 2008, 1 (1) : 101-125. doi: 10.3934/krm.2008.1.101
[9]

Lingju Kong, Roger Nichols. On principal eigenvalues of biharmonic systems. Communications on Pure & Applied Analysis, 2021, 20 (1) : 1-15. doi: 10.3934/cpaa.2020254
[10]

Fioralba Cakoni, Drossos Gintides. New results on transmission eigenvalues. Inverse Problems & Imaging, 2010, 4 (1) : 39-48. doi: 10.3934/ipi.2010.4.39
[11]

Manuel V. C. Vieira. Derivatives of eigenvalues and Jordan frames. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 115-126. doi: 10.3934/naco.2016003
[12]

Andreas Kirsch. On the existence of transmission eigenvalues. Inverse Problems & Imaging, 2009, 3 (2) : 155-172. doi: 10.3934/ipi.2009.3.155
[13]

Vesselin Petkov, Georgi Vodev. Localization of the interior transmission eigenvalues for a ball. Inverse Problems & Imaging, 2017, 11 (2) : 355-372. doi: 10.3934/ipi.2017017
[14]

Armin Lechleiter. The factorization method is independent of transmission eigenvalues. Inverse Problems & Imaging, 2009, 3 (1) : 123-138. doi: 10.3934/ipi.2009.3.123
[15]

Gianne Derks, Sara Maad, Björn Sandstede. Perturbations of embedded eigenvalues for the bilaplacian on a cylinder. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 801-821. doi: 10.3934/dcds.2008.21.801
[16]

Alexandre Girouard, Iosif Polterovich. Upper bounds for Steklov eigenvalues on surfaces. Electronic Research Announcements, 2012, 19: 77-85. doi: 10.3934/era.2012.19.77
[17]

Luc Robbiano. Counting function for interior transmission eigenvalues. Mathematical Control & Related Fields, 2016, 6 (1) : 167-183. doi: 10.3934/mcrf.2016.6.167
[18]

Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 857-869. doi: 10.3934/dcds.2004.10.857
[19]

Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487
[20]

Benoît Pausader, Walter A. Strauss. Analyticity of the nonlinear scattering operator. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 617-626. doi: 10.3934/dcds.2009.25.617

 Impact Factor: 

Tools

Metrics

  • PDF downloads (31)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences