一阶常微分方程广义初值问题解的存在性

The existence of solutions for general initial value problems of first order differential equations

运用Leray-Schauder原理和上下解方法,讨论了一阶常微分方程广义初值问题x′(t)=f(t,x(t)), a e t∈[0,T],x(0)+∫T0a(t)x(t)dt=c解的存在性.建立了该问题至少存在一个解的存在性定理.

Using the Leray-Schauder theory and upper and lower solution method,the existence of solutions for general initial value problem of first order differential equationx′(t)=f(t,x(t)),a.e.t∈, x(0)+∫~T_0a(t)x(t)dt=cis discussed, and an existence theorem of at least one solution is obtained.