带P-Laplacian算子的分数阶微分方程边值问题正解的唯一性

Uniqueness of Positive Solutions for Boundary Value Problem of Fractional Differential Equations with P-Laplacian Operator

对一类非线性项中含有线性算子与分数阶导数的分数阶P-Laplacian微分方程正解的唯一性进行了研究,其边界条件是带有分数阶导数的Riemann-Stieltjes积分边界条件.基于锥上混合单调算子的性质,根据相关算子方程的不动点定理,获得了边值问题正解的唯一性.并通过数值算例来体现主要结论的正确性与可行性.

The uniqueness of positive solutions of a class of fractional P-Laplacian differential equations with linear operators and fractional derivatives in nonlinear terms is investigated,subject to Riemann-Stieltjes integral boundary conditions which contain fractional derivatives.Based on the properties of mixed monotone operators on cone and the fixed point theorem of related operator equations,the uniqueness of positive solution of the boundary value problem is obtained.Finally,a numerical example is given as application to demonstrate the correctness the feasibility of the main conclusions.