Two-point boundary value problem for nonlinear differential equation of nth order

被引:3
|
作者
Lepin, AY
Lepin, LA
Myshkis, AD
机构
[1] Moscow State Univ Commun, Moscow 101475, Russia
[2] Latvian State Univ, Inst Math & Informat Sci, LV-1063 Riga, Latvia
基金
俄罗斯基础研究基金会;
关键词
two-point boundary value problem; nonlinear boundary value problem; differential equation of nth order;
D O I
10.1016/S0362-546X(00)85024-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The conditions of solvability and the structure of the set of solutions of the equation x(n) = f(t,x,x′, ..., x(n-1)), on a given interval [a,b] (-∞<a<b<∞) under the boundary conditions x(i)(a) = Ai (i = 0, ..., k), x(j)(b) = Bj (j = 0, ..., l) and additional restriction α(t)≤x(t)≤β(t) (a≤t≤b) were investigated. It is assumed that n≥4; the function f:[a,b]×Rn→R satisfies the Caratheodory conditions; k, l≥0; (k+1)+(l+1)≤n; α and β (α<βi.e.α(t)<β(t), for every t∈[a,b]) are solutions of x(n) = f(t,x,x′, ..., x(n-1)). The main statements are obtained as the consequence of special suppositions of the uniqueness for solutions of auxiliary boundary value problems.
引用
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页码:397 / 406
页数:10
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