Abstract
We prove that positive solutions of $-\Delta u = \lambda f(u)$ in $\Omega$ and $u = 0$ on $\partial \Omega$ where $f$ is increasing, concave, and $f(0) < 0$ satisfy $c_{1} \leq {\lambda f(d) \over d} \leq c_{2}$ where $d = \sup u.$ Also, we show that solutions of the above have exactly one inflection point.
Citation
Joseph A. Iaia. "A priori estimates and uniqueness of inflection points for positive solutions of semipositone problems." Differential Integral Equations 8 (2) 393 - 403, 1995. https://doi.org/10.57262/die/1369083476
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