具有逐项分数阶导数微分方程的非线性特征值的正解存在性  

Existence of Positive Solutions of Nonlinear Eigenvalue with Fractional Order Differential Equation

作　　者：刁林[1] Diao Lin(College of Computer Science and Technology,Shangqiu University,Shangqiu 476000,China)

机构地区：[1]商丘学院计算机工程学院,河南商丘476000

出　　处：《科技通报》2017年第5期16-19,共4页Bulletin of Science and Technology

摘　　要：在应用数学及物理学领域中分数阶微分方程使用广泛,因此研究该数学问题具有一定实用意义。于是文中将具有逐项分数阶导数微分方程当作研究目标,并对其非线性特征值的正解进行求解。首先,针对具有逐项分数阶导数的微分方程,根据Green函数性质构建微分方程基本解为边值的调和函数,并证明该方程具有非负标及有界性,再运用不动点定理对方程特征值进行区间限定;然后,利用Ri-sez-Schauder原理获取方程对应递增正特征值,对第一特征值的极值进行描述,以非线性项当作不同假设,获取分数阶微分方程解,调整参数在不同区间中,获取一个或多个特征值正解存在的必要条件。实验证明,运用文中Green函数构造方程基本解并运用Risez-Schauder原理求解非线性特征值能较好地证明其正解存在范围。Fractional differential equations are widely used in the field of Applied Mathematics andphysics.In this paper,the differential equation of fractional order derivative is taken as the researchobject,and the positive solution of the nonlinear eigenvalue is solved.First of all,according to thedifferential equation with fractional derivative one by one,according to the properties of Green functionto construct the basic solutions of differential equations with boundary value function,and prove that theequation has non negative and bounded,then by using the fixed point theorem of interval limit equationeigenvalue;then,to obtain the corresponding equation increasing positive characteristics the value ofusing Risez-Schauder principle to describe the extremum of the first eigenvalue,the nonlinear term asdifferent assumptions,obtain the fractional differential equations,adjust the parameters in differentinterval,obtain one or more feature value exists in the necessary conditions of positive solutions.Theexperimental results show that using the Green function to construct the basic solution of the equationand using the Risez-Schauder method to solve the nonlinear eigenvalue can prove the existence of thepositive solution.

关 键 词：分数阶微分方程 非线性 特征值 正解 

分 类 号：O178[理学—数学]