Dirichlet problem for second-order abstract differential equations
| dc.contributor.author | Dore, Giovanni | |
| dc.date.accessioned | 2021-10-05T22:00:38Z | |
| dc.date.available | 2021-10-05T22:00:38Z | |
| dc.date.issued | 2020-10-29 | |
| dc.description.abstract | We study the well-posedness in the space of continuous functions of the Dirichlet boundary value problem for a homogeneous linear second-order differential equation u''+ Au = 0, where A is a linear closed densely defined operator in a Banach space. We give necessary conditions for the well-posedness, in terms of the resolvent operator of A. In particular we obtain an estimate on the norm of the resolvent at the points k2, where k is a positive integer, and we show that this estimate is the best possible one, but it is not sufficient for the well-posedness of the problem. Moreover we characterize the bounded operators for which the problem is well-posed. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Dore, G. (2020). Dirichlet problem for second-order abstract differential equations. <i>Electronic Journal of Differential Equations, 2020</i>(107), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14614 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| 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 | Boundary value problem | |
| dc.subject | Differential equations in Banach spaces | |
| dc.title | Dirichlet problem for second-order abstract differential equations | |
| dc.type | Article |