Multiple Solutions of Nonlinear Boundary Value Problems for Fractional Differential Equations
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1
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In this paper, we study nonlinear boundary value problems of fractional differential equations. \begin{equation}\label{equ1} %\left\{\begin{array}{lll}\mathbf{D}_{0^{+}}^{q}x(t)=f(t,x(t))~~~~~t\in %J=[0,T]\\ %g( x(0),x(T), x(\eta))=0~~~~~~~~~ \eta\in [0,T],\end{array}\right. \begin{cases}%{lll} \mathbf{D}_{0^{+}}^{q}x(t)=f(t,x(t)) t\in J=[0,T]\\ g\big(x(0),x(T), x(\eta)\big)=0 \eta\in [0,T], \end{cases} \end{equation} where $\mathbf{D}_{0^{+}}$ denotes the Caputo fractional derivative, $0$. Some new results on the multiple solutions are obtained by the use of the Amann theorem and the method of upper and lower solutions. An example is also given to illustrate our results.
Classification :
26A33, 34K37
Zhenhai Liu; Jitai Liang. Multiple Solutions of Nonlinear Boundary Value Problems for Fractional Differential Equations. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a20/
@article{BMMS_2014_37_1_a20,
author = {Zhenhai Liu and Jitai Liang},
title = {Multiple {Solutions} of {Nonlinear} {Boundary} {Value} {Problems} for {Fractional} {Differential} {Equations}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2014},
volume = {37},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a20/}
}
TY - JOUR AU - Zhenhai Liu AU - Jitai Liang TI - Multiple Solutions of Nonlinear Boundary Value Problems for Fractional Differential Equations JO - Bulletin of the Malaysian Mathematical Society PY - 2014 VL - 37 IS - 1 UR - http://geodesic.mathdoc.fr/item/BMMS_2014_37_1_a20/ ID - BMMS_2014_37_1_a20 ER -