Abstract
We study the nonexistence of nontrivial solutions for the nonlinear elliptic system
where \((x,y,z)\in \mathbb {R}^{N_1}\times \mathbb {R}^{N_2}\times \mathbb {R}^{N_3}\), \(0<\alpha ,\beta ,\gamma ,\mu , \nu , \sigma \le 2\), \(\delta , \eta ,\theta \ge 0\), and \(p,q>1\). Here, \((-\Delta _x)^{\alpha /2}\), \(0<\alpha <2\), is the fractional Laplacian operator of order \(\alpha /2\) with respect to the variable \(x\in \mathbb {R}^{N_1}\), \((-\Delta _y)^{\beta /2}\), \(0<\beta <2\), is the fractional Laplacian operator of order \(\beta /2\) with respect to the variable \(y\in \mathbb {R}^{N_2}\), and \((-\Delta _z)^{\gamma /2}\), \(0<\gamma <2\), is the fractional Laplacian operator of order \(\gamma /2\) with respect to the variable \(z\in \mathbb {R}^{N_3}\). Using a weak formulation approach, sufficient conditions are provided in terms of space dimension and system parameters.
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This work is dedicated to the memory of Abbas Bahri
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Jleli, M., Samet, B. Liouville-type theorems for a system governed by degenerate elliptic operators of fractional orders. Arab. J. Math. 6, 201–211 (2017). https://doi.org/10.1007/s40065-016-0159-8
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DOI: https://doi.org/10.1007/s40065-016-0159-8