Cecchi, Mariella; Furi, Massimo; Marini, Mauro; Pera, Maria Patrizia Fredholm linear operators associated with ordinary differential equations on noncompact intervals. (English) Zbl 0942.34013 Electron. J. Differ. Equ. 1999, Paper No. 44, 16 p. (1999). In the noncompact interval \(J= [a,\infty)\) the authors consider a linear problem of the form \(L x=y, x\in S\), where \(L\) is a first-order differential operator, \(y\) a locally summable function in \(J\), and \(S\) a subspace of the FrĂ©chet 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, the authors 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 is reduced to the task of finding linear functionals defined in a convenient subspace of \(L_{\text{loc}}^1(J,\mathbb{R}^n)\) whose “kernel intersection” coincides with \(L(S)\). The authors 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 the results are given. Reviewer: Yujun Dong (Nanjing) MSC: 34B05 Linear boundary value problems for ordinary differential equations 47A53 (Semi-) Fredholm operators; index theories Keywords:Fredholm linear operators PDFBibTeX XMLCite \textit{M. Cecchi} et al., Electron. J. Differ. Equ. 1999, Paper No. 44, 16 p. (1999; Zbl 0942.34013) Full Text: EuDML EMIS