Existence and Concentration of Solutions for the Chern–Simons–Schrödinger System with General Nonlinearity
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DOI: 10.1007/s00025-016-0553-8
Abstract: In this paper, we study the nonlinear Chern–Simons–Schrödinger system with an external potential. Under some suitable conditions on the potential and nonlinearity, we prove the existence, multiplicity and concentration of solutions by using variational methods. read more here.
Keywords: concentration solutions; dinger system; chern simons; simons schr ... See more keywords
Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)
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DOI: 10.1186/s13661-017-0834-5
Abstract: AbstractIn this paper, we study the following coupled Schrödinger system: {−Δu+u=u2∗−1+βu2∗2−1v2∗2+f(u),x∈RN,−Δv+v=v2∗−1+βu2∗2v2∗2−1+g(v),x∈RN,u,v>0,x∈RN,$$ \textstyle\begin{cases} -\Delta u+u=u^{2^{*}-1}+\beta u^{\frac{2^{*}}{2}-1}v^{\frac {2^{*}}{2}}+f(u), &x\in\mathbb{R}^{N}, \\ -\Delta v+v=v^{2^{*}-1}+\beta u^{\frac{2^{*}}{2}}v^{\frac {2^{*}}{2}-1}+g(v), &x\in\mathbb{R}^{N}, \\ u,v>0, &x\in\mathbb{R}^{N}, \end{cases} $$ where N≥5$N\geq5$ and 2∗=2NN−2$2^{*}=\frac{2N}{N-2}$. Note that the… read more here.
Keywords: dinger system; system; frac; mathbb ... See more keywords