烟台大学学报(自然科学与工程版)
煙檯大學學報(自然科學與工程版)
연태대학학보(자연과학여공정판)
JOURNAL OF YANTAI UNIVERSITY
2002年
2期
97-103
,共7页
边值问题%非负解%存在性%不动点定理
邊值問題%非負解%存在性%不動點定理
변치문제%비부해%존재성%불동점정리
boundary value problem%nonnegative solution%existence%fixed point theorem
利用Schauder不动点定理和上下解方法,对边值问题(1)/(p(t))(p(t)y′(t))+a(t)f(t,y(t))=0,limt→0+p(t)y′(t)=0=y(1)讨论非负解的存在性. 其中p∈C1(0,1) 且在(0,1)上p>0,f≥0,对固定的y函数f(t,y)关于t是单调递减的,对固定的t函数f(t,y)关于y是单调递增的,a∈C(0,1)可以改变其符号.
利用Schauder不動點定理和上下解方法,對邊值問題(1)/(p(t))(p(t)y′(t))+a(t)f(t,y(t))=0,limt→0+p(t)y′(t)=0=y(1)討論非負解的存在性. 其中p∈C1(0,1) 且在(0,1)上p>0,f≥0,對固定的y函數f(t,y)關于t是單調遞減的,對固定的t函數f(t,y)關于y是單調遞增的,a∈C(0,1)可以改變其符號.
이용Schauder불동점정리화상하해방법,대변치문제(1)/(p(t))(p(t)y′(t))+a(t)f(t,y(t))=0,limt→0+p(t)y′(t)=0=y(1)토론비부해적존재성. 기중p∈C1(0,1) 차재(0,1)상p>0,f≥0,대고정적y함수f(t,y)관우t시단조체감적,대고정적t함수f(t,y)관우y시단조체증적,a∈C(0,1)가이개변기부호.
This paper deals with the existence of nonnegative solutions to boundary value problems (1)/(p(t))(p(t)y′(t))′+a(t)f(t,y(t))=0,limt→0+ p(t)y′(t)=0=y(1) where p∈C1 (0,1) with p>0 on (0,1),f≥0,f(t,y) is nonincreasing with respect to t for each fixed y and nondecreasing with respect to y for each fixed t,and a∈C(0,1) may change sign. Our approach is based on the Schauder fixed point theorem.
