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Infinitely many solutions for a class of fourth order elliptic equations in R N

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Abstract

With the aids of variational method and concentration-compactness principle, infinitely many solutions are obtained for a class of fourth order elliptic equations with singular potential

$$ \Delta ^2 u = \mu \frac{{|u|^{2^{**} (s) - 2} u}} {{|x|^s }} + \lambda k(x)|u|^{r - 2} u,u \in H^{2,2} (R^N ). $$

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, P. R. China

    Min Bo Yang & Zi Fei Shen

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  1. Min Bo Yang
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  2. Zi Fei Shen
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Correspondence to Min Bo Yang.

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Supported by National Science Foundation of China (10471113), Natural Science Foundation of Zhejiang Province (Y606292)

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Yang, M.B., Shen, Z.F. Infinitely many solutions for a class of fourth order elliptic equations in R N . Acta. Math. Sin.-English Ser. 24, 1269–1278 (2008). https://doi.org/10.1007/s10114-008-5423-1

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  • DOI: https://doi.org/10.1007/s10114-008-5423-1

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