Abstract: This paper deals with the Neumann problem for an elliptic
equation

$$\left\{ \begin{array}{ll} \disp -\Delta u-\frac{\mu u}{|x|^2}=\frac{|u|^{2^{*}(s)-2}u}{|x|^s}+\lambda|u|^{q-2}u, \ \ &x\in\Omega,\\ D_\gamma{u}+\alpha(x)u=0, &x\in\partial\Omega\backslash\{0\}, \end{array} \right.$$
where $\Omega$ is a bounded domain in $R^N$ with $C^1$
boundary, $0\in\partial\Omega$, $N\ge5$.
$2^{*}(s)=\frac{2(N-s)}{N-2}$ ($0\leq s\leq 2$) is the critical
Sobolev-Hardy exponent, $1 the unit outward normal to boundary $\partial\Omega$. By
variational method and the dual fountain theorem, the existence of
infinitely many solutions with negative energy is proved.

Key words: Neumann problem, Critical Sobolev-Hardy exponent, (ps)_c*condition, Dual fountain theorem

CLC Number: 

• 35J25

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