摘要
考察了含各阶导数的非线性四阶两点边值问题?u(4)(t) = f (t,u(t), u′(t), u′′(t), u′′′(t)), 0 ≤t ≤1, ? ?u′(0) = C, u′′(0) = B, u′′′(0) = A, ku(1) ? u′′′(1) = D的解和正解的存在性, 其中0 < k ≤6. 该问题的边界条件是非对称的. 四阶边值问题给出了梁振动的数学模型. 含有各阶导数的问题可以更精确地描述梁的振动. 通过构造适当的Banach空间并且利用相应的积分方程建立了两个存在定理. 主要工具是Leray-Shauder 不动点定理.论文表明, 只要非线性项f 在其定义域的某个有界子集上的“高度”是适当的, 该问题至少存在一个解或者正解.
The existence of a solution or a positive solution is considered for the nonlinear fourth-order two-point boundary value problem with all-order derivatives?u(4)(t) = f (t,u(t), u′(t), u′′(t), u′′′(t)), 0 ≤ t ≤1,??u′(0) = C, u′′(0) = B, u′′′(0) = A, ku(1) ? u′′′(1) = D where 0 < k ≤ 6. The boundary condition of this problem is nonsymmetric. The mathematical models of the vibration of beams are given by fourth-order boundary value problems. The problems with all-order derivatives can describe more precisely the vibration of beams. By constructing a suitable Banach space and applying corresponding integral equation, two existence theorems are established. The main ingredient is Leray-Schauder fixed point theorem. This paper shows that the problem has at least one solution or positive solution provided the “height” of nonlinear term f is appropriate on some bounded subset of its domain.
出处
《五邑大学学报（自然科学版）》
CAS
2005年第1期21-25,共5页
Journal of Wuyi University(Natural Science Edition)
关键词
四阶常微分方程
两点边值问题
解和正解
存在性
fourth-order ordinary differential equation
two-point boundary value problem
a solution and a positive solution
existence
