대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권2호
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  • Pages.247-262
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
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MULTIPLICITY RESULTS FOR NONLINEAR SCHRÖDINGER-POISSON SYSTEMS WITH SUBCRITICAL OR CRITICAL GROWTH

  • Guo, Shangjiang (College of Mathematics and Econometrics Hunan University) ;
  • Liu, Zhisu (School of Mathematics and Physics University of South China)
  • Received : 2014.09.27
  • Published : 2016.03.01
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Abstract

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

Keywords

References

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