Existence Results for Non-Autonomous Elliptic Boundary Value Problems
| 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.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Anuradha, V., Dickens, S., & Shivaji, R. (1994). Existence results for non-autonomous elliptic boundary value problems. <i>Electronic Journal of Differential Equations, 1994</i>(04), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7544 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| 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 | |
| dc.subject | Semipositone | |
| dc.title | Existence Results for Non-Autonomous Elliptic Boundary Value Problems | en_US |
| dc.type | Article |