caa a22 4500 606194533 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00030-014-0281-2 doi (NATIONALLICENCE)springer-10.1007/s00030-014-0281-2 Mandel Rainer Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany aut Minimal energy solutions for cooperative nonlinear Schrödinger systems [Elektronische Daten] [Rainer Mandel] We prove sharp existence and nonexistence results for minimal energy solutions of the nonlinear Schrödinger system 1 $$\left.\begin{array}{ll}\quad -\Delta u + u = |u|^{2q-2}u + b|u|^{q-2}u|v|^q \quad {\rm in} \, \mathbb{R}^{n},\\ -\Delta v + \omega^2 v = |v|^{2q-2}v + b|u|^q|v|^{q-2}v \quad {\rm in} \, \mathbb{R}^{n}\end{array}\right.$$ - Δ u + u = | u | 2 q - 2 u + b | u | q - 2 u | v | q in R n , - Δ v + ω 2 v = | v | 2 q - 2 v + b | u | q | v | q - 2 v in R n in the cooperative and subcritical case $${b > 0, 1 < q < \frac{n}{(n-2)_+}}$$ b > 0 , 1 < q < n ( n - 2 ) + . The proofs are accomplished by minimizing the Euler functional of (1) over the two associated Nehari manifolds. In the special case $${1 < q < 2}$$ 1 < q < 2 we find that a positive solution of (1) with minimal energy among all nontrivial solutions exists if and only if b>0. Springer Basel, 2014 Variational methods for elliptic systems nationallicence Nonlinear Schrödinger systems nationallicence Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/2(2015-04-01), 239-262 1021-9722 22:2<239 2015 22 30 https://doi.org/10.1007/s00030-014-0281-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-014-0281-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mandel Rainer Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/2(2015-04-01), 239-262 1021-9722 22:2<239 2015 22 30