Multiple Positive Solutions of Semi-Positone Sturm-Liouville Boundary Value Problems

This paper treats the existence of multiple positive solutionsof the semi-positone Sturm–Liouville boundary value problem. almost everywhere on R₀, R₁], where and f is allowed to take negative values (that is, f is semi-positone).When = 1, new results on the existence of one or two nonzeropositive solutions are obtained. These results generalize previousresults for positone cases (that is, f 0) to the semi-positonecases. We illustrate our results with an explicit example whichhas two nonzero positive solutions. These results are used todeduce results on intervals of eigenvalues for which there existone or two nonzero positive eigenfunctions. Applications ofthese eigenvalue results are provided. 2000 Mathematics SubjectClassification 34B18 (primary), 34B15, 34B16, 47H10, 47H30 (secondary).