We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Asymptotic behavior of normalized ground states for the fractional Schrödinger equation with combined L2‐critical and L2‐subcritical nonlinearities.
- Authors
Chen, Ruipeng; Liu, Jiayin
- Abstract
We study the asymptotic behavior of ground states for the fractional Schrödinger equation with combined L2‐critical and L2‐subcritical nonlinearities FNLS(−Δ)su+ωu=a|u|qu+|u|puinRN,N≥2with prescribed mass ‖u‖L22=c, where a∈R, 0<q<p=4sN. We first show that normalized ground states blow up as c↗c∗:=‖R‖L22, where R is the unique positive radial solution to equation (FNLS) with a=0. We then give a detailed description for the asymptotic behavior of normalized ground states as c↗c∗. Moreover, for a<0, we prove that all solutions of corresponding evolution equation with initial mass ‖R‖L2 exist globally. This result is a complement to the result of a previous study.
- Subjects
EVOLUTION equations; SCHRODINGER equation; BOLTZMANN'S equation; BEHAVIOR
- Publication
Mathematical Methods in the Applied Sciences, 2020, Vol 43, Issue 7, p4627
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.6221