Caldwell, ScottCastro, AlfonsoShivaji, R.Unsurangsie, Sumalee2021-08-132021-08-132007-06-29Caldwell, S., Castro, A., Shivaji, R., & Unsurangsie, S. (2007). Positive solutions for classes of multiparameter elliptic semipositone problems. <i>Electronic Journal of Differential Equations, 2007</i>(96), pp. 1-10.1072-6691https://hdl.handle.net/10877/14312We study positive solutions to multiparameter boundary-value problems of the form -Δu = λg(u) + μƒ(u) in Ω u = 0 on ∂Ω, where λ > 0, μ > 0, Ω ⊆ Rn; n ≥ 2 is a smooth bounded domain with ∂Ω in class C2 and Δ is the Laplacian operator. In particular, we assume g(0) > 0 and superlinear while ƒ(0) < 0, sublinear, and eventually strictly positive. For fixed μ, we establish existence and multiplicity for λ large. Our proofs are based on variational methods, the Mountain Pass Lemma, and sub-super solutions.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalPositive solutionsMultiparametersMountain pass lemmaSub-super solutionsSemipositoneArticle