CPAA
Resonant problems for fractional Laplacian
Yutong Chen Jiabao Su
Communications on Pure & Applied Analysis 2017, 16(1): 163-188 doi: 10.3934/cpaa.2017008
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.
keywords: Fractional Laplacian resonance angle condition Palais-Smale condition critical group Morse theory

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