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We found one dictionary that defines the word semipositone:

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  1. semipositone: Wiktionary

Definitions from Wiktionary (semipositone)

adjective:  (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
adjective:  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...

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