非线性分数阶微分方程边值问题正解的存在性

Abstract

Abstract:

In this paper, the authors consider the properties of Green's function for the nonlinear fractional differential equation boundary-value problem
D^α₀₊u(t)=f(t, u(t)), 0<t<1,
u(0)=u(1)=u'(0)=u'(1)=0,
where 3<α≤4 is a real number, and D^α₀₊ is the standard Riemann-Liouville differentiation, and f: [0,1]×[0, ∞)→[0, ∞) is continuous.
As an application of Green's function, the authors give some multiple positive solutions for nonlinear by means of some fixed-point theorem on cones.

Key words: Fractional differential equation, Boundary-value problem, Positive solution, Fractional Green’s function, Fixed-point theorem

CLC Number:

34B18

XU Xiao-Jie, SUN Xin-Guo, LV Wei. Existence of Positive Solutions for |Boundary Value Problems with Nonlinear Fractional Differential Equations[J].Acta mathematica scientia,Series A, 2011, 31(2): 401-409.

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Existence of Positive Solutions for |Boundary Value Problems with Nonlinear Fractional Differential Equations

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