Publicação
Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
| Resumo: | For a class of quasilinear Schr̈odinger equations with harmonic potential of the form iΦt =-ΔΦ+|x|2Φ-|Φ|p-1Φ2(Δ |Φ|2)Φt ≥ 0, x∈RN, we prove firstly the existence of stable standing waves for 1 < p < 3 + 4/N and then study the instability of standing waves for 3 + 4 /N ≤ p < 3N+2/N-2. Our results indicate that the quasilinear term (Δ|Φ|2)Φ makes the standing waves more stable than their counterpart in the semilinear case, which is consistent with the physical phenomena and is in striking contrast with the classical semilinear Schr̈odinger equations with potential. |
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| Autores principais: | Chen, Jianqing |
| Outros Autores: | Rocha, Eugénio M. |
| Assunto: | Variational methods Standing waves Stability and instability Quasilinear Schrödinger equations |
| Ano: | 2011 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| Resumo: | For a class of quasilinear Schr̈odinger equations with harmonic potential of the form iΦt =-ΔΦ+|x|2Φ-|Φ|p-1Φ2(Δ |Φ|2)Φt ≥ 0, x∈RN, we prove firstly the existence of stable standing waves for 1 < p < 3 + 4/N and then study the instability of standing waves for 3 + 4 /N ≤ p < 3N+2/N-2. Our results indicate that the quasilinear term (Δ|Φ|2)Φ makes the standing waves more stable than their counterpart in the semilinear case, which is consistent with the physical phenomena and is in striking contrast with the classical semilinear Schr̈odinger equations with potential. |
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