Fredholm Linear Operators Associated with Ordinary Differential Equations on Noncompact Intervals
| dc.contributor.author | Cecchi, Mariella | |
| dc.contributor.author | Furi, Massimo | |
| dc.contributor.author | Marini, Mauro | |
| dc.contributor.author | Pera, Maria Patrizia | |
| dc.date.accessioned | 2019-09-24T14:54:26Z | |
| dc.date.available | 2019-09-24T14:54:26Z | |
| dc.date.issued | 1999-10-31 | |
| dc.description.abstract | In the noncompact interval J = [α, ∞) we consider a linear problem of the form Lx = y, x ∈ S, where L is a first order differential operator, y a locally summable function in J, and S a subspace of the Fréchet space of the locally absolutely continuous functions in J. In the general case, the restriction of L to S is not a Fredholm operator. However, we show that, under suitable assumptions, S and L(S) can be regarded as subspaces of two quite natural spaces in such a way that L becomes a Fredholm operator between them. Then, the solvability of the problem will be reduced to the task of finding linear functionals defined in a convenient subspace of L1loc (J, ℝn) whose “kernel intersection” coincides with L(S). We will prove that, for a large class of “boundary sets” S, such functionals can be obtained by reducing the analysis to the case when the function y has compact support. Moreover, by adding a suitable stronger topological assumption on S, the functionals can be represented in an integral form. Some examples illustrating our results are given as well. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 16 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Cecchi, M., Furi, M., Marini, M., & Pera, M. P. (1999). Fredholm linear operators associated with ordinary differential equations on noncompact intervals. <i>Electronic Journal of Differential Equations, 1999</i>(44), pp. 1-16. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/8648 | |
| 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, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Fredholm operators | |
| dc.subject | Noncompact intervals | |
| dc.title | Fredholm Linear Operators Associated with Ordinary Differential Equations on Noncompact Intervals | |
| dc.type | Article |