Publication:
Positive solutions for classes of multiparameter elliptic semipositone problems

Issued Date

2007-06-29

Resource Type

Article

ISSN

10726691

Other identifier(s)

2-s2.0-34547303381

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Electronic Journal of Differential Equations. Vol.2007, (2007), 1-10

Suggested Citation

Scott Caldwell, Alfonso Castro, Ratnasingham Shivaji, Sumalee Unsurangsie Positive solutions for classes of multiparameter elliptic semipositone problems. Electronic Journal of Differential Equations. Vol.2007, (2007), 1-10. Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/24619

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Title

Positive solutions for classes of multiparameter elliptic semipositone problems

Author(s)

Scott Caldwell
 Alfonso Castro
 Ratnasingham Shivaji
 Sumalee Unsurangsie

Other Contributor(s)

Mississippi State University
 Harvey Mudd College
 Mahidol University

Abstract

We 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.

Keyword(s)

Mathematics

Availability

URI

https://repository.li.mahidol.ac.th/handle/20.500.14594/24619

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Scopus 2006-2010