山东科学
山東科學
산동과학
SHANDONG SCIENCE
2012年
1期
5-8,102
,共5页
全局分歧%特征值%两点边值
全跼分歧%特徵值%兩點邊值
전국분기%특정치%량점변치
global bifurcation%eigenvalues: two-point boundary value
讨论了边值条件为u(0)=H(1)=0的非线性两点问题-u^11(t)=.f(u(t),u^1(t)), 0〈t〈1对应的线性问题的特征值,并利用Rabinowiiz分歧定理,考虑通过(λk/f0,θ)的全局分歧理论。本文中我们允许非线性项中可以有导数项,这极大地拓展了非线性项的范围。
討論瞭邊值條件為u(0)=H(1)=0的非線性兩點問題-u^11(t)=.f(u(t),u^1(t)), 0〈t〈1對應的線性問題的特徵值,併利用Rabinowiiz分歧定理,攷慮通過(λk/f0,θ)的全跼分歧理論。本文中我們允許非線性項中可以有導數項,這極大地拓展瞭非線性項的範圍。
토론료변치조건위u(0)=H(1)=0적비선성량점문제-u^11(t)=.f(u(t),u^1(t)), 0〈t〈1대응적선성문제적특정치,병이용Rabinowiiz분기정리,고필통과(λk/f0,θ)적전국분기이론。본문중아문윤허비선성항중가이유도수항,저겁대지탁전료비선성항적범위。
Abstract : We address such non-linear two-point boundary value problem as - u^11(t) : f( u( t), u1(t) ), V 0 〈 t 〈 1, whoes boundary condition is u(O) = u( 1 ) =0. This paper investigates the eigenvalues of the linear equation corresponding to this and a global bifurcation problem through (λk/f0,θ) with Rabinowitz bifurcation theorem. We allow the existence of equations a derivative sub-term in the nonlinear term. This greatly expands the scope of the nonlinear term.