Abstract
Let Ω be a bounded smooth domain in ℝN (N ≥ 3). Assuming that 0 < s < 1, \(1 < p,q \le {{N + 2s} \over {N - 2s}}\) with \((p,q) \ne ({{N + 2s} \over {N - 2s}},{{N + 2s} \over {N - 2s}})\), and a, b > 0 are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below,
Under some assumptions of hi(x, u, v, ∇u, ∇v)(i = 1, 2), we get a priori bounds of the positive solutions to the problem (1.1) by the blow-up methods and rescaling argument. Based on these estimates and degree theory, we establish the existence of positive solutions to problem (1.1).
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This work is supported by National Natural Science Foundation of China (No.11761030), Hubei Provincial Natural Science Foundation of China (No.2022CFC016) and Cultivation Project for High-Level Scientific Research Achievements of Hubei Minzu University (No.PY20002).
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Li, Pf., Xie, Jh. & Mu, D. Existence of Positive Solutions to a Fractional-Kirchhoff System. Acta Math. Appl. Sin. Engl. Ser. 40, 225–240 (2024). https://doi.org/10.1007/s10255-024-1111-x
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DOI: https://doi.org/10.1007/s10255-024-1111-x