| Texto completo | |
| Autor(es): |
Bonheure, Denis
[1, 2]
;
Casteras, Jean-Baptiste
[1, 2]
;
dos Santos, Ederson Moreira
[3]
;
Nascimento, Robson
[1, 2]
Número total de Autores: 4
|
| Afiliação do(s) autor(es): | [1] Univ Libre Bruxelles, Dept Math, CP 214, B-1050 Brussels - Belgium
[2] INRIA Team MEPHYSTO, Brussels - Belgium
[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Número total de Afiliações: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 50, n. 5, p. 5027-5071, 2018. |
| Citações Web of Science: | 4 |
| Resumo | |
We study the mixed dispersion fourth order nonlinear Schrodinger equation i partial derivative(t)psi-gamma Delta(2)psi + beta Delta psi+vertical bar psi vertical bar(2 sigma )psi = 0 in R x R-N , where gamma, sigma > 0 and beta is an element of R. We focus on standing wave solutions, namely, solutions of the form psi(x,t) = e(i alpha t)u(x) for some alpha is an element of R. This ansatz yields the fourth order elliptic equation gamma Delta(2)u - beta Delta u +alpha u = vertical bar u vertical bar(2 sigma)u. We consider two associated constrained minimization problems: one with a constraint on the L-2-norm and the other on the L-2 sigma+ 2 -norm. Under suitable conditions, we establish existence of minimizers and we investigate their qualitative properties, namely, their sign, symmetry, and decay at infinity as well as their uniqueness, nondegeneracy, and orbital stability. (AU) | |
| Processo FAPESP: | 15/17096-6 - Problemas em EDPs elípticas: sistemas e equações |
| Beneficiário: | Ederson Moreira dos Santos |
| Linha de fomento: | Auxílio à Pesquisa - Regular |
| Processo FAPESP: | 16/50453-0 - Semilinear and quasilinear elliptic partial differential equations |
| Beneficiário: | Ederson Moreira dos Santos |
| Linha de fomento: | Auxílio à Pesquisa - Regular |