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Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights

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  • In this paper, we investigate a class of N-Laplace elliptic equations with Hardy-Sobolev operator and indefinite weights

    $ -\Delta_N u-\mu \frac{1}{(|x|\log(\frac{R}{|x|}))^N}|u|^{N-2}u= \lambda V(x)|u|^{N-2} u + f(x,u), u\in W_0^{1, N}(\Omega), $

    where $\Omega$ be a bounded domain containing $0$ in $R^N$, $N \geq 2, 0 < \mu < (\frac{N-1}{N})^N$, and the weight function $V(x)$ may change sign and has nontrivial positive part. Using Moser-Trudinger inequality and nonstandard linking structure introduced by Degiovanni and Lancelotti [6], we prove the existence of a nontrivial solution for any $\lambda\in R$.

    Mathematics Subject Classification: Primary: 35J20, 35J70; Secondary: 35J60.


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