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Zeitschrift für Analysis und ihre Anwendungen


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Volume 40, Issue 1, 2021, pp. 111–129
DOI: 10.4171/ZAA/1675

Published online: 2021-01-25

Positive Solutions for Non-Variational Fractional Elliptic Systems with Negative Exponents

Anderson L.A. de Araujo[1], Luiz F.O. Faria[2], Edir J.F. Leite[3] and Olímpio H. Miyagaki[4]

(1) Universidade Federal de Viçosa, Brazil
(2) Universidade Federal de Juiz de Fora, Brazil
(3) Universidade Federal de Viçosa, Brazil
(4) Universidade Federal de São Carlos, Brazil

In this paper, we study strongly coupled elliptic systems in non-variational form with negative exponents involving fractional Laplace operators. We investigate the existence, nonexistence, and uniqueness of the positive classical solution. The results obtained here are a natural extension of the results obtained by Ghergu [J. Funct. Anal. 258 (2010), 3295–3318] for the fractional case.

Keywords: Fractional Laplace operator, non-variational elliptic systems, negative exponents

de Araujo Anderson L.A., Faria Luiz F.O., Leite Edir J.F., Miyagaki Olímpio: Positive Solutions for Non-Variational Fractional Elliptic Systems with Negative Exponents. Z. Anal. Anwend. 40 (2021), 111-129. doi: 10.4171/ZAA/1675