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Nonnegative solution curves of semipositone problems with Dirichlet boundary conditions

✍ Scribed by G.A. Afrouzi; M. Khaleghy Moghaddam

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 152 KB
Volume: 61
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2004.08.037

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the boundary value problem

where > 0 is a parameter and f ∈ C 2 (0, ∞) is monotonically increasing and concave up such that f (0) < 0 (i.e. is the semipositone). In this paper we study the case p = and p ∈ ( , +∞). (p is the supremum of the nonnegative solution and is such that F ( ) = 0 f (s) ds = 0.) We discuss existence and multiplicity results for nonnegative solutions.

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