Existence of solutions for a BVP of a second order FDE at resonance by using Krasnoselskii's fixed point theorem on cones in the L1 space
| dc.contributor.author | Karakostas, George L. | |
| dc.contributor.author | Palaska, Konstantina | |
| dc.date.accessioned | 2022-01-03T19:30:43Z | |
| dc.date.available | 2022-01-03T19:30:43Z | |
| dc.date.issued | 2018-01-19 | |
| dc.description.abstract | We provide sufficient conditions for the existence of positive solutions of a nonlocal boundary value problem at resonance concerning a second order functional differential equation. The method is developed by inserting an exponential factor which depends on a suitable positive parameter λ. By this way a Green's kernel can be established and the problem is transformed into an operator equation u = Tλu. As it can be shown the well known Krasnoselskii's fixed point theorem is no (positive) value of the parameter λ for which the condensing property ∥Tλu∥ ≤ ∥u∥, with ∥u∥ = ρ(> 0) is satisfied. To overcome this face we enlarge the space C[0, 1] and work in L1[0, 1] where, now, Krasnoselskii's fixed point theorem is applicable. Compactness criteria in this space are, certainly, needed. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Karakostas, G. L., & Palaska, K. G. (2018). Existence of solutions for a BVP of a second order FDE at resonance by using Krasnoselskii's fixed point theorem on cones in the L1 space. <i>Electronic Journal of Differential Equations, 2018</i>(30), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15086 | |
| 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, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlocal boundary value problem | |
| dc.subject | Boundary value problems at resonance | |
| dc.subject | Second order differential equations | |
| dc.subject | Krasnoselskii's fixed point theorem on cones | |
| dc.title | Existence of solutions for a BVP of a second order FDE at resonance by using Krasnoselskii's fixed point theorem on cones in the L1 space | en_US |
| dc.type | Article |