具有积分边界条件的高阶Sturm-Liouville边值问题的可解性

Solvability of Higher Order Sturm-Liouville Boundary Value Problems with Integral Boundary Conditions

研究了具有积分边界条件的n阶Sturm-Liouville边值问题{x(n)(t)=f(t,x(t),x'(t),…,x(n-1)(t)),t∈[0,1],x(i)(0)=0,i=0,1,…,n-3,1x(n-2)(0)-ax(n-1)(0)=∫h0(s,x(s),x'(s),…,x(n-2)(s))ds,x(n-2)(1)+bx(n-1)(1)=∫h1(s,x(s),x'(s),…,x(n-2)(s))ds解的存在性,其中f∈C([0,1]×Rn),hn0,h1∈C([0,1]×R-1)并且a,b≥0为常数,利用关于两个算子和的O’Regan不动点定理,得到了上述边值问题解的存在性.

We investigated the existence of solutions for n-order Sturm-Liouville boundary value problems with integral boundary conditions {x（n）（t）=f（t,x（t）,x＇（t）,…,x（n-1）（t））,t∈[0,1],x（i）（0）=0,i=0,1,…,n-3,1x（n-2）（0）-ax（n-1）（0）=∫h0（s,x（s）,x＇（s）,…,x（n-2）（s））ds,x（n-2）（1）＋bx（n-1）（1）=∫h1（s,x（s）,x＇（s）,…,x（n-2）（s））ds where f∈C（[0,1]×Rn）,hn0,h1∈C（[0,1]×R-1） and a,b≥0 are constants. By using a fixed point theorem for the sum of two operators due to O＇ Regan, the existence of solutions for the above boundary value problems are obtained.