Abstract
Let Ω ⊂ ℝN be a ball centered at the origin with radius R > 0 and N ⩾ 7, 2* = \( \frac{{2N}} {{N - 2}} \). We obtain the existence of infinitely many radial solutions for the Dirichlet problem −Δu = \( \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u \) in Ω, u = 0 on ∂Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10526008)
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Tang, Z. Infinitely many radial solutions to elliptic problems with critical Sobolev and Hardy terms. Sci. China Ser. A-Math. 51, 1609–1618 (2008). https://doi.org/10.1007/s11425-008-0048-5
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DOI: https://doi.org/10.1007/s11425-008-0048-5