Multi-Peak Solutions for Coupled Nonlinear Schrödinger Systems in Low Dimensions
نویسندگان
چکیده
Abstract In this paper, we construct the solutions to following nonlinear Schrödinger system $$\begin{aligned} {\left\{ \begin{array}{ll} -\epsilon ^{2}\Delta u+P(x)u= \mu _{1} u^{p}+\beta u^{\frac{p-1}{2}}v^{\frac{p+1}{2}} \ \text {in} \mathbb {R}^{N},\\ v+Q(x)v= _{2} v^{p}+\beta u^{\frac{p+1}{2}}v^{\frac{p-1}{2}} {R}^{N}, \end{array}\right. } \end{aligned}$$ - ϵ 2 Δ u + P ( x ) = μ 1 p β v in R N , Q where $$3< p<+\infty $$ 3 < ∞ , $$N\in \{1,2\}$$ ∈ { } $$\epsilon >0$$ > 0 is a small parameter, potentials P Q satisfy $$0<P_{0} \le P(x)\le P_{1}$$ ≤ and ( x ) satisfies $$0<Q_{0} Q(x)\le Q_{1}$$ . We solution for attractive repulsive cases. When $$x_{0}$$ local maximum point of $$P(x_{0})=Q(x_{0})$$ k spikes concentrating near $$\overline{x}_{0}$$ ¯ u at m v when $$x_{0}\ne \overline{x}_{0}.$$ ≠ . This paper extends main results established by Peng Wang (Arch Ration Mech Anal 208:305–339, 2013) Pi (Discrete Contin Dyn Syst 36:2205–2227, 2016), authors considered case $$N=3$$ $$p=3$$
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ژورنال
عنوان ژورنال: Applied Mathematics and Optimization
سال: 2023
ISSN: ['0095-4616', '1432-0606']
DOI: https://doi.org/10.1007/s00245-023-09974-4