数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2002年
4期
364-370
,共7页
正解%不动点%阿尔采拉-阿斯卡里定理
正解%不動點%阿爾採拉-阿斯卡裏定理
정해%불동점%아이채랍-아사잡리정리
positive solution%fixed point%Arzela-Ascoli theorem
本文研究了下面这种拟线性滞后型微分方程(g(u′)′+a(t)f(ut)=0, 0＜t＜1其中g(v)=|v|p-2v,p＞1,满足非线性边界条件. 并且通过应用锥不动定理与阿尔采拉-阿斯卡里定理,证明了上述方程至少存在一个正解.
本文研究瞭下麵這種擬線性滯後型微分方程(g(u′)′+a(t)f(ut)=0, 0＜t＜1其中g(v)=|v|p-2v,p＞1,滿足非線性邊界條件. 併且通過應用錐不動定理與阿爾採拉-阿斯卡裏定理,證明瞭上述方程至少存在一箇正解.
본문연구료하면저충의선성체후형미분방정(g(u′)′+a(t)f(ut)=0, 0＜t＜1기중g(v)=|v|p-2v,p＞1,만족비선성변계조건. 병차통과응용추불동정리여아이채랍-아사잡리정리,증명료상술방정지소존재일개정해.
In this paper, we study the existence of positive solutions of the quasilinear functional delay differential equation of the form(g(u′))′+a(t)f(ut)=0, 0＜t＜1(1)where g(v)=|v|p-2v, p＞1, subject to nonlinear boundary conditions. We show that there exists at least one positive solution by applying a fixed point theorem in cones and the Arzela-Ascoli theorem.
