Exact multiplicity of positive solutions in semipositone problems with concave-convex type nonlinearities

Joseph A. Iaia, Sudhasree Gadam
2001 Electronic Journal of Qualitative Theory of Differential Equations  
We study the existence, multiplicity, and stability of positive solutions to: We consider the case when the nonlinearity f is of concave-convex type having exactly one inflection point. We establish that f should be appropriately concave ( by establishing conditions on f ) to allow multiple positive solutions. For any λ > 0, we obtain the exact number of positive solutions as a function of f (t)/t and establish how the positive solution curves to the above problem change. Also, we give examples
more » ... where our results apply. This work extends the work in [1] by giving a complete classification of positive solutions for concave-convex type nonlinearities. 1991 Mathematics Subject Classification. Primary 34B15: Secondary 35J65.
doi:10.14232/ejqtde.2001.1.4 fatcat:ueetlrta45bc5awafnro7vuq34