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.
Rights
Attribution 4.0 International