| dc.creator | Gopal, N. S. | |
| dc.creator | Jonnalagadda, J. M. | |
| dc.date | 2022-12-21 | |
| dc.identifier | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3210 | |
| dc.identifier | 10.56754/0719-0646.2403.0467 | |
| dc.description | In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated with Dirichlet boundary conditions.
\begin{align*}\begin{cases} -\big{(}\nabla^{\nu}_{\rho(a)}u\big{)}(t) + \lambda u(t) = f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a + 2}, \\u(a) = u(b) = 0, \end{cases} \end{align*}
where \(1 < \nu < 2\), \(a,b \in \mathbb{R}\) with \(b-a\in\mathbb{N}_{3}\), \(\mathbb{N}^b_{a+2} = \{a+2,a+3, . . . ,b\}\), \(|\lambda| < 1\), \(\nabla^{\nu}_{\rho(a)}u\) denotes the \(\nu^{\text{th}}\)-order Riemann–Liouville nabla difference of \(u\) based at \(\rho(a)=a-1\), and \(f : \mathbb{N}^{b}_{a + 2} \times \mathbb{R} \rightarrow \mathbb{R}^{+}\).
We make use of Guo–Krasnosels'kiÄ and Leggett–Williams fixed-point theorems on suitable cones and under appropriate conditions on the non-linear part of the difference equation. We establish sufficient requirements for at least one, at least two, and at least three positive solutions of the considered boundary value problem. We also provide an example to demonstrate the applicability of established results. | 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/3210/2261 | |
| dc.rights | Copyright (c) 2022 N. S. Gopal et al. | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 24 No. 3 (2022); 467–484 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 24 Núm. 3 (2022); 467–484 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Nabla fractional difference | en-US |
| dc.subject | boundary value problem | en-US |
| dc.subject | Dirichlet boundary conditions | en-US |
| dc.subject | positive solution | en-US |
| dc.subject | existence | en-US |
| dc.subject | fixed-point | en-US |
| dc.title | Positive solutions of nabla fractional boundary value problem | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
