Abstract
We are concerned with the following semilinear elliptic equation
$\Delta u=\lambda f\left( x,u\right) $ in $D,$ subject to some
Dirichlet conditions, where $\lambda \geq 0$ is a parameter and $D$ is
a smooth domain in $\mathbb{R}^{n}\left( n\geq 3\right) $. Under some
appropriate assumptions on the nonnegative nonlinearity term $f\left(
x,u\right) ,$ we show the existence of a positive bounded solution for
the above semilinear elliptic equation. Our approach is based on
Schauder's fixed point Theorem.