The Existence Of Solutions About Two Classes Of Nonlinear Ordinary Differential Equations

Various kinds of problems about differential equation have been mentioned in many fields of nature science. We usually set up mathematical models which depend on actual problems when solving them. In an other word, a differential equation which reflects this actual problem has been formed. Then we interpret the actual problems with the solutions of the equation and solve the actual problems. The main purpose of this article is to study the existence of the solution of two kinds of differential equations.The first section, by means of the fixed point index theory under some conditions concerning the eigenvalues corresponding to the relevant linear operator, the existence is obtained in this paper for the multi-point boundary value problem of the higher order (k, n-k) differential equation subject to the boundary value conditions respectively, where 0<ξ1<ξ2<…<ξm-2<1,ai∈[0,+∞), and h(x) is allowed to be singular at x=0 and x=1.The second section, by cone theory and fixed point index theory in semi-order Banach space of nonlinear functional analysis, the sufficient and necessary condition of the existence of periodic positive solution is obtained in this paper for one kind of multiple time-delay functional differential equation respectively, where...