含有一阶导数的四阶边值问题的正解

Positive solution to four-order boundary value problem with dependence on the first order derivative

利用锥理论和不动点指数方法,在相应算子的第一特征值有关的条件下,得到边值问题x(4)(t)+f(t,x,x')=0(0<t<1),x'(0)=x″(0)=x′″(0)=x(1)=0的正解存在性.

Applying the cone theory and the fixed point index,under the condition of the first eigenvalue of corresponding operator,we obtain the existence of positive solutions to BVP x(4)(t)+f(t,x,x′)=0(0<t<1),x′(0)=x″(0)=x′″(0)=x(1)=0.