Abstract
We consider the following critical nonhomogeneous Choquard equation
where \(\Omega \) is a smooth bounded domain of \(\mathbb {R}^N\), 0 in interior of \(\Omega \), \(\lambda \in \mathbb {R}\), \(N\ge 7\), \(0<\mu <N\), \(2_{\mu }^{*}=(2N-\mu )/(N-2)\) is the upper critical exponent in the sense of the Hardy–Littlewood–Sobolev inequality, and f(x) is a given function. Using variational methods, we obtain the existence of multiple solutions for the above problem when \(0<\lambda <\lambda _{1}\), where \(\lambda _{1}\) is the first eigenvalue of \(-\Delta \) in \(H_{0}^{1}(\Omega )\).
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Partially supported by NSFC (11571317, 11671364) and ZJNSF (LY15A010010).
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Shen, Z., Gao, F. & Yang, M. Multiple solutions for nonhomogeneous Choquard equation involving Hardy–Littlewood–Sobolev critical exponent. Z. Angew. Math. Phys. 68, 61 (2017). https://doi.org/10.1007/s00033-017-0806-8
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DOI: https://doi.org/10.1007/s00033-017-0806-8