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On Kirchhoff type problems involving critical and singular nonlinearities

Tom 114 / 2015

Chun-Yu Lei, Chang-Mu Chu, Hong-Min Suo, Chun-Lei Tang Annales Polonici Mathematici 114 (2015), 269-291 MSC: Primary 35R09; Secondary 35A15, 35B09. DOI: 10.4064/ap114-3-5

Streszczenie

In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem \begin{equation*} \cases{ -(a+b\int_\varOmega|\nabla u|^2\,dx) \varDelta u=u^{5}+\lambda\frac{u^{q-1}}{|x|^\beta} & \text{in $\varOmega$,} \cr u=0 &\text{on $\partial\varOmega$,} \cr} \end{equation*} where $\varOmega\subset \mathbb{R}^{3}$ is a smooth bounded domain, $0\in\varOmega$, $1< q<2 $, $\lambda$ is a positive parameter and $\beta$ satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

Autorzy

  • Chun-Yu LeiSchool of Sciences
    GuiZhou Minzu University
    550025 Guiyang, China
    e-mail
  • Chang-Mu ChuSchool of Sciences
    GuiZhou Minzu University
    550025 Guiyang, China
    e-mail
  • Hong-Min SuoSchool of Sciences
    GuiZhou Minzu University
    550025 Guiyang, China
    e-mail
  • Chun-Lei TangSchool of Mathematics and Statistics
    Southwest University
    400715 Chongqing, China
    e-mail

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