First extremal point comparison for a fractional boundary value problem with a fractional boundary condition
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- by Johnny Henderson and Jeffrey T. Neugebauer PDF
- Proc. Amer. Math. Soc. 147 (2019), 5323-5327 Request permission
Abstract:
Let $n \geq 2$ be a natural number, and let $n-1<\alpha \le n$ and $0<\gamma \le \alpha -1$ be real numbers. Let $\beta >0$ and $b\in (0,\beta ]$. We compare first extremal points of the differential equations $D_{0+}^\alpha u+p(t)u=0$, $D_{0+}^\alpha u+q(t)u=0$, $t\in (0,\beta )$, each of which satisfies the boundary conditions $u^{(i)}(0)=0$, $i=0,1,\dots ,n-2$, $\quad D_{0^+}^\gamma u(b)=0$. While it is assumed that $q$ is nonnegative, no sign restrictions are put on $p$. The fact that the associated Green’s function $G(b;t,s)$ is nonnegative and increasing with respect to $b$ plays an important role in the analysis.References
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Additional Information
- Johnny Henderson
- Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
- MR Author ID: 84195
- ORCID: 0000-0001-7288-5168
- Email: johnny_henderson@baylor.edu
- Jeffrey T. Neugebauer
- Affiliation: Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475
- MR Author ID: 832933
- Email: jeffrey.neugebauer@eku.edu
- Received by editor(s): January 26, 2019
- Received by editor(s) in revised form: March 13, 2019, and March 28, 2019
- Published electronically: June 14, 2019
- Communicated by: Wenxian Shen
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5323-5327
- MSC (2010): Primary 26A33, 34A08; Secondary 34A40, 26D20
- DOI: https://doi.org/10.1090/proc/14648
- MathSciNet review: 4021091