TITLE

Standing waves with a critical frequency for nonlinear Schr�dinger equations, II

AUTHOR(S)
Jaeyoung Byeon; Zhi-Qiang Wang
PUB. DATE
October 2003
SOURCE
Calculus of Variations & Partial Differential Equations;Oct2003, Vol. 18 Issue 2, p207
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
For elliptic equations of the form $\Delta u -V(\varepsilon x) u + f(u)=0, x\in {\bf R}^N$ , where the potential V satisfies $\liminf_{\vert x\vert\to \infty} V(x) > \inf_{{\bf R}^N} V(x) =0$ , we develop a new variational approach to construct localized bound state solutions concentrating at an isolated component of the local minimum of V where the minimum value of V can be positive or zero. These solutions give rise to standing wave solutions having a critical frequency for the corresponding nonlinear Schr�dinger equations. Our method allows a fairly general class of nonlinearity f( u) including ones without any growth restrictions at large.
ACCESSION #
11090216

 

Related Articles

  • Dynamical group of the relativistic Kepler problem. Horwitz, L. P. // Journal of Mathematical Physics;Feb93, Vol. 34 Issue 2, p645 

    A manifestly covariant relativistic generation of the Lenz vector for the relativistic Kepler problem is constructed. The corresponding dynamical group for the bound state problem is SO(4,1).

  • Generalization of the Birman-Schwinger method for the number of bound states. Chadan, Khosrow; Kobayashi, Reido; Lassaut, Monique // Journal of Mathematical Physics;Apr99, Vol. 40 Issue 4, p1756 

    Focuses on the generalization of the Birman-Schwinger method. Derivation of a general upper bound on the number of bound states in the S wave for a spherically symmetric potential; Invention of the Birman-Schwinger method in order to put the Lippmann-Schwinger equation of scattering theory on...

  • Algebraic solution for the Natanzon hypergeometric potentials. Cordero, Patricio; Salamó, Sebastián // Journal of Mathematical Physics;Jul94, Vol. 35 Issue 7, p3301 

    An algebraic method—based on a strategy that makes use of a realization of the algebra SO(2,1)—in terms of differential operators is used to solve the bound state problem for the most general Natanzon potentials for which the Schrödinger equation can be reduced to hypergeometric...

  • Bound states, resonances, and symmetries of a neutral Dirac particle with anomalous magnetic moment, coupled to a fixed monopole. Barut, A. O.; Bracken, A. J. // Journal of Mathematical Physics;Jun85, Vol. 26 Issue 6, p1390 

    For the system consisting of a neutral Dirac particle with anomalous magnetic moment, interacting with a fixed magnetic monopole, zero-energy bound states are constructed for each possible value of the total angular momentum. Results of Kazama and Yang for the chargemonopole system are used to...

  • Pohozaev obstructions on non-starlike domains. Jeff McGough; Jeff Mortensen // Calculus of Variations & Partial Differential Equations;Oct2003, Vol. 18 Issue 2, p189 

    This paper investigates the existence of a Pohozaev obstruction on non-starlike domains. The elliptic problems we examine are of the form $$\begin{array}{rl}\displaystyle \rm div\left\{\, g(x, \nabla u) \right\} + \lambda f(x,u) = 0, & x\in\Omega , \\\displaystyle u = 0, & x\in\partial\Omega ,...

  • Non-Smooth Solutions for a Class of Infinitely Degenerate Elliptic Differential Equations. Nguyen Minh Tri // Vietnam Journal of Mathematics;Jun2000, Vol. 28 Issue 2, p159 

    Examines the non-smooth solutions for a class of infinitely degenerate elliptic differential equations. Definition of notations; Establishment of the auxiliary lemmas; Construction of the explicit global non-smooth solutions.

  • Optical and magneto-optical properties of Co(001)/Ge/Co sandwiches. Kang, S. S.; Jin, G. J.; Xu, X. N.; Hu, A.; Zhai, H. R.; Jiang, S. S.; Chen, Y.; Zhu, W. R.; Dong, G. S.; Zhou, S. M.; Jin, X.; Feng, J. W. // Applied Physics Letters;12/16/1996, Vol. 69 Issue 25, p3923 

    A series of bcc-Co(001)/Ge/Co trilayers was grown on a GaAs(001) substrate by the molecular beam epitaxy technique. The optical and magneto-optical properties of the samples were studied. An oscillatory variation of the magneto-optical Kerr effect (MOKE) with the thickness of the Ge spacers was...

  • Regularity Results for Linear Elliptic Problems Related to the Primitive Equations. Hu, Changbing; Temam, R.; Ziane, M. // Chinese Annals of Mathematics;Apr2002, Vol. 23 Issue 2, p277 

    The authors study the regularity of solutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the Primitive Equations of the ocean. The present work generalizes the regularity results in [18] by taking into consideration the...

  • Inverse scattering by a local impurity in a periodic potential in one dimension. II. Newton, Roger G. // Journal of Mathematical Physics;Feb85, Vol. 26 Issue 2, p311 

    This paper continues and completes the solution to the inverse scattering problem initiated in a recent paper. It allows for the existence of bound states in the band gaps and corrects a number of errors in the first paper.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sign out of this library

Other Topics