一类无穷区间上的三阶两点边值问题解的存在性

Existence of Solutions for a Third-Order Two-Point Boundary Value Problem on Infinite Intervals

研究一类无穷区间上的三阶两点边值问题:{x′″(t)+a(t)f(t,x(t),x'(t),x″(t))=0,t∈(0,+∞),x(0)=0,x'(0)-bx″(0)=0,x″(+∞)=c,其中a∈C([0,+∞),(0,+∞)),f∈C([0,+∞)×R^3,R),b≥0,c∈R.综合运用上下解方法和Schauder不动点定理,得到了上述三阶无穷边值问题解的存在性.

We concerned with a third-order two-point boundary value problem on infinite intervals of the form x?(t)+a(t)f(t,x(t),x′(t),x″(t))=0,t∈(0,+￥),x(0)=0,x′(0)-bx″(0)=0,x″(+￥)=c,{where a∈C([0,+∞),(0,+∞)),f∈C([0,+∞)×R3,R),b≥0,c∈R.The existence of solution is obtained by using the upper and lower solution method together with Schauder fixed point theorem for the above third-order infinite boundary value problem.