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Ground-state solution for a class of biharmonic equations including critical exponent

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Abstract

In this paper, we study the following biharmonic equations

$$\Delta^2 u = \lambda{\frac{|u|^{2^{\ast\ast}(s)-2}u}{|x|^s}} + \beta a(x)|u|^{r-2}u,\quad x\in {\mathbb{R}}^N.$$

Under some suitable assumptions of \({\lambda}\), \({\beta}\) and \({a(x)}\), the existence of ground-state solution and nonexistence of nontrivial solution are obtained by using variational methods. Moreover, the phenomenon of concentration of solutions is also explored.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Hongliang Liu & Haibo Chen

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  1. Hongliang Liu
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  2. Haibo Chen
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Correspondence to Hongliang Liu.

Additional information

Research supported by Hunan Provincial Foundation For Postgraduate CX2014B044, Natural Science Foundation of China 11271372 and Mathematics and Interdisciplinary Sciences Project of CSU.

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Liu, H., Chen, H. Ground-state solution for a class of biharmonic equations including critical exponent. Z. Angew. Math. Phys. 66, 3333–3343 (2015). https://doi.org/10.1007/s00033-015-0583-1

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  • DOI: https://doi.org/10.1007/s00033-015-0583-1

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