dc.contributor.author Anuradha, V. ( ) dc.contributor.author Dickens, S. ( ) dc.contributor.author Shivaji, R. ( ) dc.date.accessioned 2018-08-17T16:14:35Z dc.date.available 2018-08-17T16:14:35Z dc.date.issued 1994-07-08 dc.identifier.citation Anuradha, V., Dickens, S., & Shivaji, R. (1994). Existence results for non-autonomous elliptic boundary value problems. Electronic Journal of Differential Equations, 1994(04), pp. 1-10. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/7544 dc.description.abstract We study solutions to the boundary value problems `−∆u(x) = λf (x, u); x ∈ Ω` `u(x) + α(x) ∂u(x) / ∂n = 0; x ∈ ∂Ω` where λ > 0, Ω is a bounded region in ℝN ; N ≥ 1 with smooth boundary ∂Ω, α(x) ≥ 0, n is the outward unit normal, and f is a smooth function such that it has either sublinear or restricted linear growth in u at infinity, uniformly in x. We also consider f such that f (x, u)u ≤ 0 uniformly in x, when |u| is large. Without requiring any sign condition on f (x, 0), thus allowing for both positone as well as semipositone structure, we discuss the existence of at least three solutions for given λ ∈ (λn, λn+1) where λk is the k-th eigenvalue of −∆ subject to the above boundary conditions. In particular, one of the solutions we obtain has non-zero positive part, while another has non-zero negative part. We also discuss the existence of three solutions where one of them is positive, while another is negative, for λ near λ1, and for λ large when f is sublinear. We use the method of sub-super solutions to establish our existence results. We further discuss non-existence results for λ small. en_US dc.format Text dc.format.extent 10 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Southwest Texas State University, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 1994, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Elliptic boundary value problems en_US dc.subject Semipositone en_US dc.title Existence Results for Non-Autonomous Elliptic Boundary Value Problems en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License.
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