有序Banach空间中非线性二阶周期边值问题的正解

POSITIVE SOLUTIONS FOR NONLINEAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEMS IN ORDERED BANACH SPACES

讨论了有序Banach空间E中的非线性二阶周期边值问题-u″(t)+bu′(t)+cu(t)=f(t,u(t)),0≤t≤ω,u(0)=u(ω),u′(0)=u′(ω)正解的存在性,其中b,c∈R且c>0,f:[0,ω]×P→P连续,P为E中的正元锥.本文通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论,获得了该问题正解的存在性结果.

The existence of positive solutions for nonlinear second order periodic boundary value problems -u″（t）＋bu′（t）＋cu（t）=f（t,u（t））,0≤t≤ω,u（0）=u（ω）,u′（0）=u′（ω） in an ordered Banach spaces E was discussed,where b, c∈R, and c 〉 0, f（t, x） ： [0,ω] × P → P is continuous, and P is the cone of positive elements in E. An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.