文档介绍：
On the existence of multiple positive solutions to boundary
value problems of nonlinear fractional differential equations
WANG Libo, XU Guigui*
5
10
15
20
(School of Mathematical Science, Kaili University, GuiZhou KaiLi 556011)
Abstract: In this paper, we study the existence of multiple positive solutions for the nonlinear
fractional differential equation boundary value problem. By the properties of the Green function, the
lower and upper solution method and fixed point theorem, some new existence criteria for fractional
di_erential equation boundary value problem are established.
Keywords: ODE; Boundary value problems; Green function; Positive solution; Fractional
differerential equation
0 Introduction
Fractional differential equations have been of great interest recently , see [1-4].. It is caused
both by the intensive development of the theory of fractional calculus itself and by the applications,
It should be noted that most of papers and books on fractional calculus are devoted to the
solvability of linear initial fractional differential equations on terms of special functions,see[5-9].
Recently, there are some papers dealing with the existence of solutions, .[10-13] (or positive
solutions, see [14-18]) of nonlinear initial (or singular and nonsingular boundary) value problems
of fractional differential equation by the use of techniques of nonlinear analysis (fixed-point
theorems, Leray-Schauder theory, lower and upper solution method, Adomian position
method etc.), see[18-22].
Bai and Lv [16] studied the following two-point boundary value problem of fractional
differential equations
D0á+ (u) + f (t, u(t)) = 0,
0 < t < 1,
25
u(0) = u(1) = 0,
Where 1 < á ≤ 2 is a real number and D0á+ is the standard Riemann-Liouville fractional
derivative. They obtained the existence of positive solutions by means of Guo-Krasnosel'skii
fixed point theorem and Leggett-Williams fixed point theorem.
Liang and Zhang [18] investigated the fol