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Resonant problems for fractional Laplacian

  • Author Bio: E-mail address: chenyutong@cnu.edu.cn; E-mail address: sujb@cnu.edu.cn
Supported by KZ201510028032 and NSFC11601353,11671026.
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  • In this paper we consider the following fractional Laplacian equation

    $ \left\{\begin{array}{ll} (-\Delta).s u=g(x, u) & x\in\Omega,\\ u=0, & x \in \mathbb{R}.N\setminus\Omega,\end{array} \right. $

    where $ s\in (0, 1)$ is fixed, $\Omega$ is an open bounded set of $\mathbb{R}.N$, $N > 2s$, with smooth boundary, $(-\Delta).s$ is the fractional Laplace operator. By Morse theory we obtain the existence of nontrivial weak solutions when the problem is resonant at both infinity and zero.

    Mathematics Subject Classification: 49J35, 35A15, 35S15, 45G25, 58E05.


    \begin{equation} \\ \end{equation}
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