一、理论基础 矿区地下水动态可视为一灰色系统,可以建立灰色系统模型,来进行研究和预测其动态。 建立灰色模型方法: 一个n阶、h个变量的灰色模型,可记作GM（n,h）。模型,形式为: sum from i=0 to n(ai(d<sup>n-1</sup>...一、理论基础 矿区地下水动态可视为一灰色系统,可以建立灰色系统模型,来进行研究和预测其动态。 建立灰色模型方法: 一个n阶、h个变量的灰色模型,可记作GM（n,h）。模型,形式为: sum from i=0 to n(ai(d<sup>n-1</sup>(x<sub>1</sub><sup>1</sup>)/dt<sup>n-1</sup>=sum from i=1 to h<sub>1</sub>(b<sub>i</sub>X<sub>i+1</sub><sup>1</sup>…（1）式中 n—微分方程的阶数; h—变量个数。 一般来讲,作为灰色系统预测模型的形式为GM（n,1）,这里的1是个变量。进行地下水动态变化分析和预测时只需研究一个变量,即地下水水位变量。 现以GM（1,1）模型为例,简述其建模方法。建立的模型为连续的（或离散的）微分模型,第一步,引入微分方程模型的形式为:展开更多
By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value prob...By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.展开更多
文摘一、理论基础 矿区地下水动态可视为一灰色系统,可以建立灰色系统模型,来进行研究和预测其动态。 建立灰色模型方法: 一个n阶、h个变量的灰色模型,可记作GM（n,h）。模型,形式为: sum from i=0 to n(ai(d<sup>n-1</sup>(x<sub>1</sub><sup>1</sup>)/dt<sup>n-1</sup>=sum from i=1 to h<sub>1</sub>(b<sub>i</sub>X<sub>i+1</sub><sup>1</sup>…（1）式中 n—微分方程的阶数; h—变量个数。 一般来讲,作为灰色系统预测模型的形式为GM（n,1）,这里的1是个变量。进行地下水动态变化分析和预测时只需研究一个变量,即地下水水位变量。 现以GM（1,1）模型为例,简述其建模方法。建立的模型为连续的（或离散的）微分模型,第一步,引入微分方程模型的形式为:
基金Foundation item： the National Natural Science Foundation of China （No. 10671167） the Natural Science Foundation of Liaocheng University （No. 31805）.
文摘By constructing a special cone and applying the fixed point theorem of cone compression and expansion,this paper investigates the existence of positive solutions for a class of first order singular boundary value problem(BVP,for short) on unbounded domains.Moreover,an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.
