非线性2n阶微分方程的非线性两点边值问题解的存在性

摘要

利用上下解的方法研究了非线性2n阶常微分方程Y~((2n))=f(t,y,y',…,y~((2n-1))满足如下边界条件条件g_0(y(a),y'(a))=0,g_1(y'(a),y"(a),…,y~((2n-3))(a))=0,g_2(y~((2n-2))(a),y~((2n-1))(a))=0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),Y(i+1)(c))=0(i=3,4,…,2n-2).的非线性两点边值问题解的存在性.%By using the method of upper-lower solutions,the sufficient conditions are given for the existence of solutions to nonlinear two point boundary value problems for nonlinear 2nth-order differential equation y~((2n))=f(t,y,y',...,y~((2n-1))) with the boundary conditions g_0(y(a),y'(a)) =0,g_1(y'(a),y"(a),...,y~((2n-3))(a)) =0,g_2(y~((2n-2))(a),y~((2n-1))(a)) =0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),y~((i+1))(c))=0(i=3,4,...,2n-2).