Multiple solutions for elliptic problems with singular and sublinear potentials

Abstract:

For certain positive numbers $\mu$ and $\lambda ,$ we establish the multiplicity of solutions to the problem \[ \left \{ \begin {array}{lll} -\triangle u=\mu \frac {u}{|x|^2}+\lambda f(u)& \textrm {a.e.\ in} \ \Omega , u=0 & \textrm {on}\ \partial \Omega , \end {array}\right . \] where $\Omega$ is a bounded open domain in $\mathbb {R}^N\ (N\geq 3)$ containing the origin with smooth boundary $\partial \Omega ,$ while $f:\mathbb {R}\to \mathbb {R}$ is continuous, superlinear at zero and sublinear at infinity.