Positive solutions for classes of multiparameter elliptic semipositone problems

Date

2007-06-29

Authors

Caldwell, Scott
Castro, Alfonso
Shivaji, R.
Unsurangsie, Sumalee

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

We 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.

Description

Keywords

Positive solutions, Multiparameters, Mountain pass lemma, Sub-super solutions, Semipositone

Citation

Caldwell, 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.

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Attribution 4.0 International

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