semipositone
adjEtymology From semi- + positone.
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Mathematics, Sciences 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 formLeszek Gasinski; Nikolaos S. Papageorgiou (2004), Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, CRC Press, page 704
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for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...