一类四阶常微分方程的正解

Positive Solutions of a Fourth-order Ordinary Differential Equation

讨论了四阶常微分方程边值问题u( 4) +βu″-αu =φ(t) f (u) ,u(0 ) =u(1) =u″(0 ) =u″(1) =0的正解存在性 ,利用锥拉伸与压缩不动点定理 ,给出了至少有一个正解存在的充分条件 ,并且建立了多个正解的存在性结果 .

The existence of positive solutions of the fourth order boundary value problem  u (4) +βu″-α(u) =φ(t)f(u),u(0)=u(1)=u″(0)=u″(1)=0 is discussed. By using the fixed point theorem in cone, sufficient conditions are given for this problem which has at least one positive solution, and several existence theorems of multiple positive solutions are established.