Infinite semipositone problems with asymptotically linear growth forcing terms
Infinite semipositone problems with asymptotically linear growth forcing terms
We study the existence of positive solutions to the singular problem \begin{equation*} \begin{cases} -\Delta_p u = \lambda f(u)-\frac{1}{u^{\alpha}} & \mbox{ in } \Omega, \\ u = 0 & \mbox{ on } \partial \Omega, \end{cases} \end{equation*} where $\lambda$ is a positive parameter, $\Delta_p u =\operatorname{div}(|\nabla{u}|^{p-2}\nabla{u})$, $p > 1$, $\Omega $ is …