Standing waves for a coupled system of nonlinear Schrödinger equations
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0371-5 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0371-5 | ||
| 245 | 0 | 0 | |a Standing waves for a coupled system of nonlinear Schrödinger equations |h [Elektronische Daten] |c [Zhijie Chen, Wenming Zou] |
| 520 | 3 | |a 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 . | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Coupled Schrodinger equations |2 nationallicence | |
| 690 | 7 | |a Semiclassical states |2 nationallicence | |
| 690 | 7 | |a General nonlinearity |2 nationallicence | |
| 690 | 7 | |a Variational methods |2 nationallicence | |
| 700 | 1 | |a Chen |D Zhijie |u Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China |4 aut | |
| 700 | 1 | |a Zou |D Wenming |u Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 183-220 |x 0373-3114 |q 194:1<183 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0371-5 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0371-5 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chen |D Zhijie |u Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zou |D Wenming |u Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/1(2015-02-01), 183-220 |x 0373-3114 |q 194:1<183 |1 2015 |2 194 |o 10231 | ||