佳木斯大学学报（自然科学版）
佳木斯大學學報（自然科學版）
가목사대학학보（자연과학판）
Journal of Jiamusi University(Natural Science Edition)
2015年
5期
730-732
,共3页
拟线性微分方程%非极端解%最终正解
擬線性微分方程%非極耑解%最終正解
의선성미분방정%비겁단해%최종정해
quasilinear differential equation%non-extreme solution%eventually positive solution
大多数的拟线性微分方程不能写出其解的表达式,所以对解的性质的研究就显得尤为重要.研究了一类三阶拟线性微分方程非极端解的存在性.其中利用函数的单调性、积分计算以及积分换元等微积分知识研究了非极端解存在的必要性,利用Schauder-Tychonoff不动点定理研究了非极端解存在的充分性,得到了非极端解存在的充分必要条件.所得结果拓展了前人的结果.
大多數的擬線性微分方程不能寫齣其解的錶達式,所以對解的性質的研究就顯得尤為重要.研究瞭一類三階擬線性微分方程非極耑解的存在性.其中利用函數的單調性、積分計算以及積分換元等微積分知識研究瞭非極耑解存在的必要性,利用Schauder-Tychonoff不動點定理研究瞭非極耑解存在的充分性,得到瞭非極耑解存在的充分必要條件.所得結果拓展瞭前人的結果.
대다수적의선성미분방정불능사출기해적표체식,소이대해적성질적연구취현득우위중요.연구료일류삼계의선성미분방정비겁단해적존재성.기중이용함수적단조성、적분계산이급적분환원등미적분지식연구료비겁단해존재적필요성,이용Schauder-Tychonoff불동점정리연구료비겁단해존재적충분성,득도료비겁단해존재적충분필요조건.소득결과탁전료전인적결과.
Most of the quasilinear differential equation cannot indicate the expression of its solution, so it is very important to study the properties of the solution.This paper is concerned with the existence of non-ex-treme solution of one type third-order quasilinear differential equation.The necessity of the existence of non-extreme solution is studied by using the calculus.The sufficiency of the existence of non-extreme solution is studied by using the Schauder-Tychonoff fixed point theorem.This paper obtained a necessary and sufficient condition with non-extreme solution of the third -order quasilinear differential equation.The result comple-ments and extends previously known ones.
