含p-Laplacian无穷点边值问题正解的存在性

Positive solutions for an infinite-point boundary value problem with p-Laplacian operators

含p-Laplacian算子的微分方程在物理学、计算机科学和图像处理等领域有着广泛的应用.基于Riemann-Liouville导数的分数阶微分方程,该文研究了一类含p-Laplacian算子的无穷多点边值问题.通过求解等价积分方程,得到对应的格林函数及其性质,最后通过线性算子的谱半径及迭代方法,得到边值问题正解的存在唯一性,并举例验证所得结果的有效性.

Nowadays,differential equations with p-Laplacian operator has been adapted to numerous fields,such as physics,computer science and picture processing.On the basis of Riemann-Liouville derivatives,in this paper,a class of infinite-point boundary value problem with p-Laplacian operator is studied.Green’s functions of integral equation and properties are obtained by solving the integral equation which is equivalent to differential equation.Finally,the existence and uniqueness of positive solutions to boundary value problems is proved by the spectral radius and iterative technique to the linear operators,and examine the efficiency for the results via examples.