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Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents

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Abstract

Let Ω ⊂ ℝN be a smooth bounded domain such that 0 ∈ Ω,N≥3, 0≤s<2,2* (s)=2(N−s)/(N−2). We prove the existence of nontrival solutions for the singular critical problem\( - \Delta u - \mu \frac{u}{{\left| x \right|^2 }} = \frac{{\left| u \right|^{2^* \left( s \right) - 2} }}{{\left| x \right|^s }}u + \lambda u\) with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.

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Authors and Affiliations

  1. Department of Mathematics, South-Central University For Nationalities, 430074, Wuhan, P.R. China

    Dongsheng Kang

  2. Department of Mathematics, Xiaogan University, 432100, Xiaogan, P.R. China

    Shuangjie Peng

  3. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 430071, Wuhan, P.R. China

    Shuangjie Peng

Authors
  1. Dongsheng Kang
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  2. Shuangjie Peng
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Correspondence to Dongsheng Kang.

Additional information

Corresponding author. This work is supported partly by the National Natural Science Foundation of China (No. 10171036) and the Natural Science Foundation of South-Central University For Nationalities (No. YZZ03001). The authors sincerely thank Prof. Daomin Cao (AMSS, Chinese Academy of Sciences) for helpful discussions and suggestions.

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Kang, D., Peng, S. Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents. Isr. J. Math. 143, 281–297 (2004). https://doi.org/10.1007/BF02803503

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  • DOI: https://doi.org/10.1007/BF02803503

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