کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591500 | 1335033 | 2011 | 22 صفحه PDF | دانلود رایگان |
In this paper we develop a new method to prove the existence of minimizers for a class of constrained minimization problems on Hilbert spaces that are invariant under translations. Our method permits to exclude the dichotomy of the minimizing sequences for a large class of functionals. We introduce family of maps, called scaling paths, that permits to show the strong subadditivity inequality. As byproduct the strong convergence of the minimizing sequences (up to translations) is proved. We give an application to the energy functional I associated to the Schrödinger–Poisson equation in R3R3iψt+Δψ−(|x|−1⁎|ψ|2)ψ+|ψ|p−2ψ=0iψt+Δψ−(|x|−1⁎|ψ|2)ψ+|ψ|p−2ψ=0 when 2
0ρ>0. In this way we recover the case studied in Sanchez and Soler (2004) [20] for p=8/3p=8/3 and we complete the case studied by the authors for 3
Journal: Journal of Functional Analysis - Volume 261, Issue 9, 1 November 2011, Pages 2486–2507