semipositone

Adjective
\begin{cases} -\Delta x(z) = \lambda f (x (z)) \text { for a.a. }z \in \Omega, \\ x|_{\partial \Omega},\ x \ge 0 \end{cases} $$
 * 1)  an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
 * Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
 * Finally, we mention that several papers studied nonlinear eigenvalue problems of the form
 * for $$\scriptstyle \lambda\ >\ 0 $$ under the assumption that $$\scriptstyle f:\ \mathbb R\ \to\ \mathbb R$$ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity $$\scriptstyle f:\ \mathbb R\ \to\ \mathbb R$$ is continuous, monotone and $$\scriptstyle f(0)\ <\ 0 $$,...then the eigenvalue problem is called semipositone...