一类三阶常微分方程的两点边值问题的正解

Positive Solutions to a Class of Two-point Boundary Value Problem of Third-order Ordinary Differential Equations

利用Krasnoselskii不动点定理讨论三阶常微分方程两点边值问题{um(t)+f(t,u(t))=0,t∈[0,1],u(0)=u'(0)=u'(1)=0正解的存在性与多重性,其中f:[0,1]×[0,∞)→[0,∞)连续.采用不等式条件代替以往的极限条件描述非线性的增长条件.

By using the Krasnoselskii＇ s fixed point theorem,we investigate the existence and multiplicity of positive solutions for third-order two-point boundary value problem {u＇＇＇（t） ＋f（＇t,u（t））=0,t ∈ [0,1],u（0） =u （0） =u＇（1） =0,where f：[0,1] × [0,∞） → [0,∞） is continuous.In this work,the limit conditions are replaced by the inequality conditions to describe the nonlinear growth.