  We study existence and nonexistence of strictly positive solutions for the
elliptic problems of the form $Lu=m\left( x\right) u^{p}$ in a bounded open
interval, with zero boundary conditions, where $L$ is a strongly uniformly
elliptic differential operator, $p\in\left( 0,1\right) $, and $m$ is a function
that changes sign. We also characterize the set of values $p$ for which the
problem admits a solution, and in addition an existence result for other
nonlinearities is presented.
