Abstract
By a semipositone problem we mean a semilinear equation where the nonlinearity is nondecreasing and negative at the origin. A typical example is the Dirichlet problem
whereλ ∈ (0,∞) is a parameter, Ω is a smooth bounded region in ℝn, Δ is the Laplacian operator and f: ℝ → ℝ is a locally Lipschitzian monotonically increasing function such that
and f(σ)> 0 for some σ >0. Semipositone problems naturally arise in various studies.
Supported in part by NSF Grant DMS - 8905936
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© 1993 Springer Science+Business Media Dordrecht
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Castro, A., Shivaji, R. (1993). Semipositone problems. In: Goldstein, G.R., Goldstein, J.A. (eds) Semigroups of Linear and Nonlinear Operations and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1888-0_4
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