Existence and nonexistence of radial solutions for semilinear equations with bounded nonlinearities on exterior domains
| dc.contributor.author | Iaia, Joseph | |
| dc.date.accessioned | 2021-10-11T17:05:56Z | |
| dc.date.available | 2021-10-11T17:05:56Z | |
| dc.date.issued | 2020-12-01 | |
| dc.description.abstract | In this article we study radial solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R > 0 centered at the origin in ℝN where ƒ is odd with ƒ < 0 on (0, β), ƒ > 0 on (β, δ), ƒ ≡ 0 for u > δ, and where the function K(r) is assumed to be positive and K(r) → 0 as r → ∞. The primitive F(u) = ∫u0 ƒ(t) dt has a "hilltop" at u = δ. With mild assumptions on ƒ we prove that if K(r) ~ r-α with 2 < α < 2(N - 1) then there are n solutions of Δu + K(r)ƒ(u) = 0 on the exterior of the ball of radius R such that u → 0 as r → ∞ if R > 0 is sufficiently small. We also show there are no solutions if R > 0 is sufficiently large. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Iaia, J. (2020). Existence and nonexistence of radial solutions for semilinear equations with bounded nonlinearities on exterior domains. <i>Electronic Journal of Differential Equations, 2020</i>(117), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14628 | |
| dc.language.iso | en | |
| dc.publisher | 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, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Sublinear equation | |
| dc.subject | Radial solution | |
| dc.subject | Exterior domain | |
| dc.title | Existence and nonexistence of radial solutions for semilinear equations with bounded nonlinearities on exterior domains | |
| dc.type | Article |