Multiple Solutions for Some Elliptic Equations With a Nonlinearity Concave in the Origin

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem\[\begin{array}{lll}-\Delta u = -\lambda |u|^{q-2}u +au+g(u) & {\rm in} & \Omega\\ \ \ \ \ u = 0 & {\rm on} & \partial \Omega,\end{array}\]where $\Omega \subset \mathbb{R}^N$ is a bounded domain with smooth boundary $\partial \Omega$, $g:\mathbb{R}\to \mathbb{R}$ is a function of class $C^1$ such that $g(0)=g'(0)=0$, $\lambda>0$ is real parameter, $a\in\R$, and $1