Positive solutions of nabla fractional boundary value problem
نویسندگان
چکیده
In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated Dirichlet conditions. \begin{equation*} \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{equation*} where $1 < \nu 2$, $a,b \mathbb{R}$ $b-a\in\mathbb{N}_{3}$, $\mathbb{N}^b_{a+2} \{a+2,a+3,\hdots,b\}$, $|\lambda| 1$, $\nabla^{\nu}_{\rho(a)}u$ denotes $\nu^{\text{th}}$-order Riemann--Liouville nabla difference of $u$ based at $\rho(a)=a-1$, and $f : 2} \times \mathbb{R} \rightarrow \mathbb{R}^{+}$. We make use Guo--Krasnosels'ki\v{\i} Leggett--Williams fixed-point theorems on suitable cones under appropriate conditions non-linear part equation. establish sufficient requirements for least one, two, three positive solutions considered problem. also provide an example to demonstrate applicability established results.
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ژورنال
عنوان ژورنال: Cubo
سال: 2022
ISSN: ['0716-7776', '0719-0646']
DOI: https://doi.org/10.56754/0719-0646.2403.0467