n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果
Acta Mathematicae Applicatae Sinica(2003)
Abstract
本文利用上、下解方法讨论了n阶非线性常微分方程满足下列非线性边界条件(2)及(3)的边值问题解的存在性.{g1(y(d0),y'(d0),...,y(n-2)(d0)) = 0,g2(y(d1),y'(d1),...,y(n-2)(d1)) =0,gn-2(y(dn-3),y'(dn-3),……,y(n-2)(dn-3)) =0,gn-1(y(a),y'(a),...,y(n-1)(a)) =0,gn(y(b),y'(b),...,y(n-1)(b)) =0,(2)其中di=a或di=b (0=0,1,…,n-3),且di取值各自独立.a∈R,b∈R,a<b.它包含2n-2个不同类型的边界条件.{y1(y(d0),y'(d0),...,y(n-2)(d0)) =0,g2(y(d1),y'(d1),……,y(n-2)(d1)) =0,gn-2(y(dn-3),y'(dn-3),……,y(n-2)(dn-3)) =0,gn-1(y(a),y'(a),...,y(n-1)(a)) =0,gn(y(c),y'(c),...,y(n-1)(c)) =0,(3)其中di=a或di=b或di=c (i=0,1,…,n-3),di取值各自独立,且至少有一个di=b(0≤i≤n-3).a∈R,b∈R c∈R,a<b<c.它包含2@3n-3个不同类型的边界条件.[1-4]中的许多结果都为本文特例.
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Key words
point boundary value problems,differential equations,nonlinear,solutions,further existence results,nth-order
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