Aijun Yang, Johnny Henderson, Charles Nelms Jr.
Abstract:
The Krein-Rutman theorem is applied to establish the extremal point,
,
for a higher-order Riemann-Liouville fractional equation,
,
,
,
,
under the boundary conditions
,
,
.
The key argument is that a mapping,
which maps a linear, compact operator, depending on
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.
Submitted May 19, 2015. Published June 16, 2015.
Math Subject Classifications: 26A33, 34B08, 34B40.
Key Words: u-positive operator; fractional boundary value problem;
spectral radius
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Aijun Yang Zhejiang University of Technology College of Science Hangzhou 310023, China email: yangaij2004@163.com, Aijun_Yang@baylor.edu | |
Johnny Henderson Department of Mathematics, Baylor University Waco, TX 76798-7328, USA email: Johnny_Henderson@baylor.edu | |
Charles Nelms Jr. Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA email: Charles_Nelms@baylor.edu |
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