\ In this paper, the following biharmonic elliptic problem \begin{ eqnarray*} \begin{ cases} \Delta^2u-\lambda\frac{ |u|^{ q-2}u}{ |x|^s}=|u|^{ 2^{ **}-2}u+ f(x,u), &x\in\Omega,\\ u=\dfrac{ \partial u}{ \partial n}=0, &x\in\partial\Omega \end{ cases} \end{ eqnarray*} is considered. The main feature of the equation is that it involves a Hardy term and a nonlinearity with critical Sobolev exponent. By combining a careful analysis of the fibering maps of the energy functional associated with the problem with the Mountain Pass Lemma, it is shown, for some positive parameter $\lambda$ depending on $s$ and $q$, that the problem admits at least one mountain pass type solution under appropriate growth conditions on the nonlinearity $f(x,u)$.
Categories: math.AP