Existence of Solutions for a System of Second-order Four-dimensional Differential Equations

摘要

In this paper, we deal with the existence of solutions of a class of boundary value problems for a system of second-order four-dimensional differential equations under the certain conditions: ｛-u" = f(x,u,v,m,n),-v"=g(x,u,v,m,n),-m" = h(x, u, v),-n" = w( x,u, v),u(0) = u(1) = v(0) = v(1) = m(0) = m(1) = n(0) = n(1) = 0 The method of Schauder fixpoint theorem is discussed in the paper.