一类扰动Gelfand问题正解的存在性及其性质  

Existence and Properties of Positive Solutions for a Class of Perturbed Gelfand Problem

作　　者：翟成波[1] 鞠盈盈 ZHAI Chengbo;JU Yingying(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第3期543-547,共5页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(201901D111020)。

摘　　要：该文通过锥理论、增算子不动点定理以及单调迭代技巧得出扰动Gelfand问题正解的存在性,改进和推广了关于该问题已有的结论,即给其参数λ一个具体范围,使其有解且该解有下界,并用一种不同的方法得出了解的一些性质:关于参数具有单调性和渐近性。In this paper,by using the cone theory,fixed point theorems for increasing operators,and monotone iterative techniques,we obtain the existence of positive solutions for a perturbed Gelfand problem,which generalizes the known conclusion about this problem,that is,we give a specific range of the parameter λ,in which there exist solutions and the solutions have a lower bound.In addition,by a different method we present some properties of the solutions which include monotonicity and asymptotic property with respect to the parameter.

关 键 词：Gelfand问题 正解 增算子 不动点定理 正规锥 

分 类 号：O175[理学—数学]