Semiclassical states of nonlinear Schrödinger equations with bounded potentials

Antonio Ambrosetti; Marino Badiale; Silvia Cingolani

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 3, page 155-160
  • ISSN: 1120-6330

Abstract

top
Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential V .

How to cite

top

Ambrosetti, Antonio, Badiale, Marino, and Cingolani, Silvia. "Semiclassical states of nonlinear Schrödinger equations with bounded potentials." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.3 (1996): 155-160. <http://eudml.org/doc/244295>.

@article{Ambrosetti1996,
abstract = {Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential \( V \).},
author = {Ambrosetti, Antonio, Badiale, Marino, Cingolani, Silvia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nonlinear Schrödinger equations; Critical point theory; Homoclinic solutions; nonlinear Schrödinger equations; critical point theory; homoclinic solutions},
language = {eng},
month = {12},
number = {3},
pages = {155-160},
publisher = {Accademia Nazionale dei Lincei},
title = {Semiclassical states of nonlinear Schrödinger equations with bounded potentials},
url = {http://eudml.org/doc/244295},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Ambrosetti, Antonio
AU - Badiale, Marino
AU - Cingolani, Silvia
TI - Semiclassical states of nonlinear Schrödinger equations with bounded potentials
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 3
SP - 155
EP - 160
AB - Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential \( V \).
LA - eng
KW - Nonlinear Schrödinger equations; Critical point theory; Homoclinic solutions; nonlinear Schrödinger equations; critical point theory; homoclinic solutions
UR - http://eudml.org/doc/244295
ER -

References

top
  1. AMBROSETTI, A. - BADIALE, M. - CINGOLANI, S., Semiclassical states of nonlinear Schrödinger equations. To appear. Zbl0896.35042
  2. AMBROSETTI, A. - COTI ZELATI, V. - EKELAND, I., Symmetry breaking in Hamiltonian systems. Jour. Diff. Equat., 67, 1987, 165-184. Zbl0606.58043MR879691DOI10.1016/0022-0396(87)90144-6
  3. DEL PINO, M. - FELMER, P., Local mountain passes for semilinear elliptic problems in unbounded domains. Cal Var., 4, 1996, 121-137. Zbl0844.35032MR1379196DOI10.1007/BF01189950
  4. FLOER, A. - WEINSTEIN, A., Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. Jour. Funct. Anal., 69, 1986, 397-408. Zbl0613.35076MR867665DOI10.1016/0022-1236(86)90096-0
  5. GRILLAKIS, M. - SHATAH, J. - STRAUSS, W., Stability theory of solitary waves in the presence of symmetry. Jour. Funct. Anal., 74, 1987, 160-197. Zbl0656.35122MR901236DOI10.1016/0022-1236(87)90044-9
  6. GUI, C., Multi-bump solutions for nonlinear Schrödinger equations. C. R. Acad. Sci. Paris, 322, 1966, 133-138. Zbl0839.35038MR1373749
  7. KWONG, M. K., Uniqueness of positive solutions of Δ ⁢ u ⁢ — ⁢ u + u p = 0 in R N . Arch. Rational Mech. Anal., 105, 1989, 243-266. Zbl0676.35032MR969899DOI10.1007/BF00251502
  8. OH, Y. G., Existence of semiclassical bound states of nonlinear Schrödinger equations with potential in the class V a . Comm. Partial Diff. Eq., 13, 1988, 1499-1519. Zbl0702.35228MR970154DOI10.1080/03605308808820585
  9. OH, Y. G., Stability of semi-classical bound states of nonlinear Schrödinger equations with potentials. Comm. Math. Phys., 121, 1989, 11-33. Zbl0693.35132MR985612
  10. RABINOWTTZ, P. H., On a class of nonlinear Schrödinger equations. ZAMP, 43, 1992, 271-291. 
  11. WANG, X., On concentration of positive bound states of nonlinear Schrödinger equations. Comm. Math. Phys., 153, 1993, 223-243. Zbl0795.35118MR1218300

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.