semipositone

== English == === Etymology === From semi- +‎ positone. === Adjective === semipositone (not comparable) (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero. Leszek Gasinski; Nikolaos S. Papageorgiou (2004), Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, CRC Press, →ISBN, page 704 Finally, we mention that several papers studied nonlinear eigenvalue problems of the form { − Δ x ( z ) = λ f ( x ( z ) ) for a.a. z ∈ Ω , x | ∂ Ω , x ≥ 0 {\displaystyle {\begin{cases}-\Delta x(z)=\lambda f(x(z)){\text{ for a.a. }}z\in \Omega ,\\x|_{\partial \Omega },\ x\geq 0\end{cases}}} for λ > 0 {\displaystyle \scriptstyle \lambda \ >\ 0} under the assumption that f : R → R {\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} } is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity f : R → R {\displaystyle \scriptstyle f:\ \mathbb {R} \ \to \ \mathbb {R} } is continuous, monotone and f ( 0 ) < 0 {\displaystyle \scriptstyle f(0)\ <\ 0} ,...then the eigenvalue problem is called semipositone...