Semiclassical states of nonlinear Schrödinger equations with bounded potentials
Ambrosetti, Antonio ; Badiale, Marino ; Cingolani, Silvia
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996), p. 155-160 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

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.

Usando dei risultati di perturbazione nella teoria dei punti critici, si prova che alcune equazioni di Schrödinger nonlineari hanno stati semiclassici che si concentrano vicino ai punti critici del potenziale V.

Publié le : 1996-12-01
@article{RLIN_1996_9_7_3_155_0,
     author = {Antonio Ambrosetti and Marino Badiale and Silvia Cingolani},
     title = {Semiclassical states of nonlinear Schr\"odinger equations with bounded potentials},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {7},
     year = {1996},
     pages = {155-160},
     zbl = {0872.35098},
     mrnumber = {1454410},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1996_9_7_3_155_0}
}

Ambrosetti, Antonio; Badiale, Marino; 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, Tome 7 (1996) pp. 155-160. http://gdmltest.u-ga.fr/item/RLIN_1996_9_7_3_155_0/

[1] Ambrosetti, A. - Badiale, M. - Cingolani, S., Semiclassical states of nonlinear Schrödinger equations. To appear. | Zbl 0896.35042

[2] Ambrosetti, A. - Coti Zelati, V. - Ekeland, I., Symmetry breaking in Hamiltonian systems. Jour. Diff. Equat., 67, 1987, 165-184. | MR 879691 | Zbl 0606.58043

[3] Del Pino, M. - Felmer, P., Local mountain passes for semilinear elliptic problems in unbounded domains. Cal Var., 4, 1996, 121-137. | MR 1379196 | Zbl 0844.35032

[4] Floer, A. - Weinstein, A., Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. Jour. Funct. Anal., 69, 1986, 397-408. | MR 867665 | Zbl 0613.35076

[5] Grillakis, M. - Shatah, J. - Strauss, W., Stability theory of solitary waves in the presence of symmetry. Jour. Funct. Anal., 74, 1987, 160-197. | MR 901236 | Zbl 0656.35122

[6] Gui, C., Multi-bump solutions for nonlinear Schrödinger equations. C. R. Acad. Sci. Paris, 322, 1966, 133-138. | MR 1373749 | Zbl 0839.35038

[7] Kwong, M. K., Uniqueness of positive solutions of Δ⁢u⁢—⁢u+up=0 in RN. Arch. Rational Mech. Anal., 105, 1989, 243-266. | MR 969899 | Zbl 0676.35032

[8] Oh, Y. G., Existence of semiclassical bound states of nonlinear Schrödinger equations with potential in the class Va. Comm. Partial Diff. Eq., 13, 1988, 1499-1519. | MR 970154 | Zbl 0702.35228

[9] Oh, Y. G., Stability of semi-classical bound states of nonlinear Schrödinger equations with potentials. Comm. Math. Phys., 121, 1989, 11-33. | MR 985612 | Zbl 0693.35132

[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. | MR 1218300 | Zbl 0795.35118