Geodesic
Extremal points for a higher-order fractional boundary-value problem
Electronic journal of differential equations, Tome 2015 (2015)
The Krein-Rutman theorem is applied to establish the extremal point, $b_0$, for a higher-order Riemann-Liouville fractional equation, $D_{0+}^{\alpha}y+p(t)y = 0, 0 $, under the boundary conditions $y^{(i)}(0)= 0, y^{(n-1)}(b) = 0, i=0,1,2,\ldots, n-1$. The key argument is that a mapping, which maps a linear, compact operator, depending on $b$ to its spectral radius, is continuous and strictly increasing as a function of b. Furthermore, we also treat a nonlinear problem as an application of the result for the extremal point for the linear case.
Classification : 26A33, 34B08, 34B40
Keywords: u-positive operator, fractional boundary value problem, spectral radius 
@article{EJDE_2015__2015__a73,
     author = {Yang,  Aijun and Henderson,  Johnny and Nelms,  Charles jun.},
     title = {Extremal points for a higher-order fractional boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1334.34023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a73/}
}
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%A Nelms,  Charles jun.
%T Extremal points for a higher-order fractional boundary-value problem
%J Electronic journal of differential equations
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%F EJDE_2015__2015__a73
Yang,  Aijun; Henderson,  Johnny; Nelms,  Charles jun. Extremal points for a higher-order fractional boundary-value problem. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a73/