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Singular positive solutions for a fourth order elliptic problem in $R$

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  • In this paper, we consider the following fourth order elliptic problem in $R^N$:

    $\Delta^2 u-c_1\Delta u+c_2 u=u^p+\kappa \sum_{i=1}^m \alpha_i \delta_{a_i}$ in $\mathcal D'(R^N),$

    $ u(x)>0, u(x) \rightarrow 0 $ as $ |x| \rightarrow \infty. $

    We will prove if $0 < \kappa < \kappa^* $ for some $\kappa^*\in (0,\infty)$, then this problem has at least two singular positive solutions.

    Mathematics Subject Classification: Primary: 35J35; Secondary: 35J60.


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