Evolution of positive solution curves in semipositone problems with concave nonlinearities. (English) Zbl 0985.34014
The authors examine existence, multiplicity and stability of positive solutions to a Dirichlet boundary value problem for a particular one-dimensional second-order nonlinear ordinary differential equation. They establish certain conditions on the nonlinear component of the equation, which allow for multiple positive solutions and under an appropriate assumption to establish the number of positive solutions. Examples illustrating the theory are provided.
Reviewer: Nikolai L.Vulchanov (Warszawa)
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34L30 | Nonlinear ordinary differential operators |
Keywords:
nonlinear boundary value problems; second-order one-dimensional equation; Dirichlet boundary; existence; multiplicity; stability of solutionsReferences:
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