Abstract
In this paper, we investigate the existence of nontrivial solution for the following class of Choquard equation
where \(N\in {\mathbb {N}},~N\ge 3,~\alpha \in (0,N),~I_\alpha \) is a Riesz potential, \(\lambda >0\) is a parameter, \(p=\frac{N+\alpha }{N-2}\) is the upper Hardy–Littlewood–Sobolev critical exponent and \(q\in (2,\frac{2N}{N-2}).\) We prove that there exists \(\lambda _0>0\) such that for \(\lambda \ge \lambda _0,\) problem (1) possesses one positive radial solution.
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Supported by National Natural Science Foundation of China (no. 11471267); Fundamental Research Funds for the Central Universities (no. XDJK2016E116)
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Pan, HL., Liu, J. & Tang, CL. Existence of a Positive Solution for a Class of Choquard Equation with Upper Critical Exponent. Differ Equ Dyn Syst 30, 51–59 (2022). https://doi.org/10.1007/s12591-018-0437-3
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DOI: https://doi.org/10.1007/s12591-018-0437-3