Existence of positive solutions for nonlinear boundary-value problems in unbounded domains of Rn
| dc.contributor.author | Toumi, Faten | |
| dc.contributor.author | Zeddini, Noureddine | |
| dc.date.accessioned | 2021-07-13T20:34:37Z | |
| dc.date.available | 2021-07-13T20:34:37Z | |
| dc.date.issued | 2005-12-08 | |
| dc.description.abstract | Let D be an unbounded domain in ℝn (n ≥ 2) with a nonempty compact boundary ∂D. We consider the following nonlinear elliptic problem, in the sense of distributions, Δu = ƒ(., u), u > 0 in D, u|∂D = αφ, lim|x|→+∞ u(x)/h(x) = βλ, where α, β, λ are nonnegative constants with α + β > 0 and φ is a nontrivial nonnegative continuous function on ∂D. The function ƒ is nonnegative and satisfies some appropriate conditions related to a Kato class of functions, and <i>h</i> is a fixed harmonic function in D, continuous on ¯D. Our aim is to prove the existence of positive continuous solutions bounded below by a harmonic function. For this aim we use the Schauder fixed-point argument and a potential theory approach. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Toumi, F., Zeddini, N. (2005). Existence of positive solutions for nonlinear boundary-value problems in unbounded domains of . <i>Electronic Journal of Differential Equations, 2005</i>(143), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13868 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, 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, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Green function | |
| dc.subject | Nonlinear elliptic equation | |
| dc.subject | Positive solution | |
| dc.subject | Schauder fixed point theorem | |
| dc.title | Existence of positive solutions for nonlinear boundary-value problems in unbounded domains of Rn | |
| dc.type | Article |