Scott CaldwellAlfonso CastroRatnasingham ShivajiSumalee UnsurangsieMississippi State UniversityHarvey Mudd CollegeMahidol University2018-08-242018-08-242007-06-29Electronic Journal of Differential Equations. Vol.2007, (2007), 1-10107266912-s2.0-34547303381https://repository.li.mahidol.ac.th/handle/20.500.14594/24619We study positive solutions to multiparameter boundary-value problems of the form -Δu = λg(u) + μf(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 C2and Δ is the Laplacian operator. In particular, we assume g(0) > 0 and superlinear while f(0) < O, sublinear, and eventually strictly positive. For fixed μ, we establish existence and multiplicity for A small, and nonexistence for A large. Our proofs are based on variational methods, the Mountain Pass Lemma, and sub-super solutions. © 2007 Texas State University.Mahidol UniversityMathematicsArticleSCOPUS