**MSC:**- 35-XX Partial differential equations

elliptic equation $(-\Delta +q)u=\lambda \rho u+f(x,u)$ in $\Rset^{N}$ under

the hypothesis that $N\geq 3,\; q(x)\to +\infty\quad\mbox{as}\quad

|x|\to +\infty$ and $\rho \in L^{\frac{N}{2}}(\Rset^{N}).$

Similar results for semilinear systems of $n$ equations are also established.