摘要
This paper is concerned with the following n-th ordinary differential equation:{u～(n)(t)=f(t,u(t),u～(1)(t),···,u～(n-1) (t)),for t∈(0,1),u～(i) (0)=0,0 ≤i≤n3,au～(n-2)(0)du～(n-1)(0)=0,cu～(n-2)(1)+du～(n-1)(1)=0,where a,c ∈ R,,≥,such that a～2 + b～2 >0 and c～2+d～2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.
This paper is concerned with the following n-th ordinary differential equation：{u～（n）（t）=f（t,u（t）,u～（1）（t）,···,u～（n-1） （t））,for t∈（0,1）,u～（i） （0）=0,0 ≤i≤n3,au～（n-2）（0）du～（n-1）（0）=0,cu～（n-2）（1）＋du～（n-1）（1）=0,where a,c ∈ R,,≥,such that a～2 ＋ b～2 〉0 and c～2＋d～2〉0,n ≥ 2,f：[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique.
