Positive solutions for classes of multiparameter elliptic semipositone problems

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dc.contributor.authorCaldwell, Scott
dc.contributor.authorCastro, Alfonso
dc.contributor.authorShivaji, R.
dc.contributor.authorUnsurangsie, Sumalee
dc.date.accessioned2021-08-13T16:00:40Z
dc.date.available2021-08-13T16:00:40Z
dc.date.issued2007-06-29
dc.description.abstractWe 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationCaldwell, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14312
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectPositive solutions
dc.subjectMultiparameters
dc.subjectMountain pass lemma
dc.subjectSub-super solutions
dc.subjectSemipositone
dc.titlePositive solutions for classes of multiparameter elliptic semipositone problems
dc.typeArticle

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