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

AbstractIn this paper, we study the following biharmonic equations $$\Delta^2 u = \lambda{\frac{|u|^{2^{\ast\ast}(s)-2}u}{|x|^s}} + \beta a(x)|u|^{r-2}u,\quad x\in {\mathbb{R}}^N.$$Δ2u=λ|u|2**(s)-2u|x|s+βa(x)|u|r-2u,x∈RN.Under some suitable assumptions of $${\lambda}$$λ, $${\beta}$$β and $${a(x)}$$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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