Positive solutions for classes of multiparameter elliptic semipositone problems
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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.
CitationCaldwell, S., Castro, A., Shivaji, R., & Unsurangsie, S. (2007). Positive solutions for classes of multiparameter elliptic semipositone problems. Electronic Journal of Differential Equations, 2007(96), pp. 1-10.
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