caa a22 4500 605495920 CHVBK 20210128100533.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10231-013-0371-5 doi (NATIONALLICENCE)springer-10.1007/s10231-013-0371-5 Standing waves for a coupled system of nonlinear Schrödinger equations [Elektronische Daten] [Zhijie Chen, Wenming Zou] We study the following system of nonlinear Schrödinger equations: $$\begin{aligned} \left\{ \begin{array}{l} -\varepsilon ^2\Delta u +a(x) u = f(u)+\lambda v, \quad x\in \mathbb R ^N, \\ -\varepsilon ^2\Delta v +b(x) v =g(v)+\lambda u, \quad x\in \mathbb R ^N,\\ u,v >0 \,\,\,\hbox {in}\,\,\,\mathbb R ^N,\quad u, v \in H^1 (\mathbb R ^N), \end{array}\right. \end{aligned}$$ - ε 2 Δ u + a ( x ) u = f ( u ) + λ v , x ∈ R N , - ε 2 Δ v + b ( x ) v = g ( v ) + λ u , x ∈ R N , u , v > 0 in R N , u , v ∈ H 1 ( R N ) , where $$N\ge 3$$ N ≥ 3 , $$\varepsilon , \lambda >0$$ ε , λ > 0 , and $$a, b, f, g$$ a , b , f , g are continuous functions. Under very general assumptions on both the potentials $$a, b$$ a , b and the nonlinearities $$f, g$$ f , g , for small $$\lambda >0$$ λ > 0 and $$\varepsilon >0$$ ε > 0 , we obtain positive solutions of this coupled system via pure variational methods. The asymptotic behaviors of these solutions are also studied either as $$\varepsilon \rightarrow 0$$ ε → 0 or as $$\lambda \rightarrow 0$$ λ → 0 . Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Coupled Schrodinger equations nationallicence Semiclassical states nationallicence General nonlinearity nationallicence Variational methods nationallicence Chen Zhijie Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China aut Zou Wenming Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 183-220 0373-3114 194:1<183 2015 194 10231 https://doi.org/10.1007/s10231-013-0371-5 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/s10231-013-0371-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Zhijie Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 700 1- Zou Wenming Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/1(2015-02-01), 183-220 0373-3114 194:1<183 2015 194 10231