CAJ | 학술논문

研究奇异半正定性分数阶格林微分方程正多解。分数阶格林微分方程正多解对于许多实际数学应用中的优化正多解寻找具有很好的指导意义。传统的格林微分方程正多解分析方法采用正定模型下的正定正多解分析方法，只能适用于较少数的特殊情况，对于许多模型不具有很好的代表意义。研究一种奇异半正定性分数阶格林微分方程正多解分析方法，在格林函数微分方程正多解分析的基础上，对于正多解的范围进行奇异半正定性的限定分析，通过推到论证，得出正多解分析结果，由于具有广泛的代表意义，此方法对于许多数学应用具有很好的指导意义。
연구기이반정정성분수계격림미분방정정다해。분수계격림미분방정정다해대우허다실제수학응용중적우화정다해심조구유흔호적지도의의。전통적격림미분방정정다해분석방법채용정정모형하적정정정다해분석방법，지능괄용우교소수적특수정황，대우허다모형불구유흔호적대표의의。연구일충기이반정정성분수계격림미분방정정다해분석방법，재격림함수미분방정정다해분석적기출상，대우정다해적범위진행기이반정정성적한정분석，통과추도론증，득출정다해분석결과，유우구유엄범적대표의의，차방법대우허다수학응용구유흔호적지도의의。
The multiple solutions analysis of differential equations of fractional Green with singular semi-positive definiteness was researched. The fractional Green differential equations were important for many practical applications of mathematical optimization, and it had good guidance for seeking multiple solutions. In traditional Green differential analysis methods, the multiple solutions were used for multiple solutions with analytical methods definite positive definite model, it can only used in a relatively small number of exceptional cases, while in the other models, it did not had very good representative of significance. So the multiple solutions analysis of differential equations of fractional green with singular semi-positive definiteness was researched, on the basis of the Green's function analysis, the differential equations were analyzed with multiple solutions for and range of positive analysis, and the analysis were limited to half the positive definiteness of the singular, by pushing the argument, the positive results of the analysis of multiple solutions were obtained, the solutions have significance application value for a broad representation, so this method can be used in many applications of mathematics and it has good guidance value.