Banach空间积-微分方程两点边值问题的解

Solutions of two-point boundary value problems of integro-differential equations in Banach spaces

利用混合单调算子理论及一个新的比较定理讨论了Banach空间积-微分两点边值问题:-u″=f(t,u,Tu,Su),au(0)-bu′(0)=x0,cu(1)+du′(1)=x1.解的存在唯一性,其中a,b,c,d 0,δ=ac+ad+bc,I=[0,1],x0,x1∈E且f∈C[I×E×E×E,E],Tu(t)=∫0tk(t,s)u(s)ds,Su(t)=∫01h(t,s)u(s)ds,t∈I,k∈C(D,R+),D={(t,s)∈I×I,t s},h∈C(I×I,R+),R+=[0,∞).

In this paper, The existence and uniqueness of the solution for the two-point boundary value problem for integro-differential equations in Banach spaces{-u^n=f（t,u,Tu,Su）au（0）-bu＇（0）=x0,cu（1）＋du＇（1）=x1 are discussed by use of mixed monotone operator theory and a new comparision theorem,where a,b,c,d≥0,δ=ac＋ad＋bc,I=[0,1],x0,x1∈E且f∈C[I×E×E×E,E],Tu（t）=∫0^1k（t,s）u（s）ds,Su（t）=∫0^1h（t,s）u（s）ds,任意t∈I,k∈C（D,R）,D={（t,s）∈I×I,t≥s},h∈C（I×I,R.）,R=[0,∞）.