一类两端简单支撑弹性梁问题解的存在性  

Existence of solutions for a class of elastic beam problems with simply supported ends

作　　者：马亚薇 马如云 MA Ya-Wei;MA Ru-Yun(School of Mathematics and Statistics,Xidian University,Xi’an710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《四川大学学报（自然科学版）》2022年第2期15-19,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12061064)。

摘　　要：本文研究了一类两端简单支撑的弹性梁问题{y″″(x)+(k 1(x)+k 2(x))y″(x)+k 1(x)k 2(x)y(x)=f(x,y(x)),0<x<1,y(0)=y(1)=y″(0)=y″(1)=0}解的存在性,其中的函数k j∈C[0,1],j=1,2,且对于任意的x∈[0,1]存在正常数h_(1),h_(2)满足0<k_(1)(x)<h_(1)<k_(2)(x)<h_(2)<t_(1)^(2)≈4.11585,t_(1)是方程t cos t+sin t=0的第一个正解.主要结果的证明基于上下解方法和Elias不等式.problems with simply supported ends MA Ya-Wei,MA Ru-Yun(School of Mathematics and Statistics,Xidian University,Xi’an 710126,China)We in this paper study the existence of solutions for the following elastic beam problem with simply supported ends:y″″(x)+(k 1(x)+k 2(x))y″(x)+k 1(x)k 2(x)y(x)=f(x,y(x)),0<x<1,y(0)=y(1)=y″(0)=y″(1)=0,where k_(j)∈C[0,1],j=1,2 and for any x∈[0,1]there exist positive constants h_(1),h_(2) satisfying 0<k_(1)(x)<h_(1)<k_(2)(x)<h_(2)<t_(1)^(2)≈4.11585,t_(1) is the first positive solution of the equation t cos t+sin t=0.The proof of the main results is based on the method of lower and upper solutions and the Elias’s inequality.

关 键 词：弹性梁方程 非共轭 上下解方法 存在性 

分 类 号：O175.8[理学—数学]