| dc.creator | Eloe, Paul W. | |
| dc.creator | Neugebauer, Jeffrey T. | |
| dc.date | 2023-08-07 | |
| dc.date.accessioned | 2023-12-19T18:55:51Z | |
| dc.date.available | 2023-12-19T18:55:51Z | |
| dc.identifier | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3446 | |
| dc.identifier | 10.56754/0719-0646.2502.251 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/239188 | |
| dc.description | It has been shown that, under suitable hypotheses, boundary value problems of the form, \(Ly+\lambda y=f,\) \(BC y =0\) where \(L\) is a linear ordinary or partial differential operator and \(BC\) denotes a linear boundary operator, then there exists \(\Lambda >0\) such that \(f\ge 0\) implies \(\lambda y \ge 0\) for \(\lambda\in [-\Lambda ,\Lambda ]\setminus\{0\},\) where \(y\) is the unique solution of \(Ly+\lambda y=f,\) \(BC y =0\). So, the boundary value problem satisfies a maximum principle for \(\lambda\in [-\Lambda ,0)\) and the boundary value problem satisfies an anti-maximum principle for \(\lambda\in (0, \Lambda ]\). In an abstract result, we shall provide suitable hypotheses such that boundary value problems of the form, \(D_{0}^{\alpha}y+\beta D_{0}^{\alpha -1}y=f,\) \(BC y =0\) where \(D_{0}^{\alpha}\) is a Riemann-Liouville fractional differentiable operator of order \(\alpha\), \(1<\alpha \le 2\), and \(BC\) denotes a linear boundary operator, then there exists \(\mathcal{B} >0\) such that \(f\ge 0\) implies \(\beta D_{0}^{\alpha -1}y \ge 0\) for \(\beta \in [-\mathcal{B} ,\mathcal{B} ]\setminus\{0\},\) where \(y\) is the unique solution of \(D_{0}^{\alpha}y+\beta D_{0}^{\alpha -1}y =f,\) \(BC y =0\). Two examples are provided in which the hypotheses of the abstract theorem are satisfied to obtain the sign property of \(\beta D_{0}^{\alpha -1}y.\) The boundary conditions are chosen so that with further analysis a sign property of \(\beta y\) is also obtained. One application of monotone methods is developed to illustrate the utility of the abstract result. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3446/2302 | |
| dc.rights | Copyright (c) 2023 P. W. Eloe et al. | en-US |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 25 No. 2 (2023); 251–272 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 25 No. 2 (2023); 251–272 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Maximum principle | en-US |
| dc.subject | anti-maximum principle | en-US |
| dc.subject | Riemann-Liouville fractional differential equation | en-US |
| dc.subject | boundary value problem | en-US |
| dc.subject | monotone methods | en-US |
| dc.subject | upper and lower solution | en-US |
| dc.subject | 34B08 | en-US |
| dc.subject | 34B18 | en-US |
| dc.subject | 34B27 | en-US |
| dc.subject | 34L15 | en-US |
| dc.title | Maximum, anti-maximum principles and monotone methods for boundary value problems for Riemann-Liouville fractional differential equations in neighborhoods of simple eigenvalues | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
