| Texto completo | |
| Autor(es): |
Campos, Luccas
;
Murphy, Jason
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 55, n. 4, p. 37-pg., 2023-01-01. |
| Resumo | |
We consider the focusing inhomogeneous nonlinear Schr & ouml;dinger equation in H-1(R-3) , i partial derivative(t)u +Delta u+|x|(-b)|u|(2)u=0 , where 0<b<1/2 . Previous works (see, e.g., [L. Campos, Nonlinear Anal., 202 (2021), 112118; L. G. Farah and C. M. Guzm & aacute;n, J. Differential Equations, 262 (2017), pp. 4175-4231; J. Murphy, Proc. Amer. Math. Soc., 150 (2022), pp. 1177-1186]) have established a blowup/scattering dichotomy below a mass-energy threshold determined by the ground state solution Q . In this work, we study solutions exactly at this mass-energy threshold. In addition to the ground state solution, we prove the existence of solutions Q(+/-) , which approach the standing wave in the positive time direction but either blow up or scatter in the negative time direction. Using these particular solutions, we classify all possible behaviors for threshold solutions. In particular, the solution either behaves as in the subthreshold case, or it agrees with e(it) , Q(+) , or Q(-) up to the symmetries of the equation. (AU) | |
| Processo FAPESP: | 20/10185-1 - Comportamento local e global de soluções de equações dispersivas |
| Beneficiário: | Luccas Cassimiro Campos |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |