| Contents |
| We consider positive solutions to classes of steady state reaction diffusion equations of the form
$$\begin{array}{rcl}
-\Delta_p u & = & \lambda f(u); \; \Omega\\
u & = & 0; \; \partial \Omega\\
\end{array}$$
where $\Delta_p z := \text{div}\left(\left|\nabla z\right|^{p-2}\nabla z\right)$; $p > 1$ is the $p$--Laplacian of $z$, $\Omega$ is a smooth bounded domain in ${\mathbb R}^N$; $N \geq 1$, $\lambda$ is a positive parameter and $f: (0, \infty) \rightarrow {\mathbb R}$ is a class of $C^1$ functions such that $\lim_{s \rightarrow 0^+} f(s) = -\infty$ (infinite semipositone case). We establish existence results via the method of sub-super solutions. We also discuss results for classes of systems of equations with infinite semipositone structure. |
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