二阶两点微分方程系统多个正解的存在性

Existence of Multiple Positive Solutions for Systems of Second-order Two-point ODE

利用一个改进的L eggett-W illiam s不动点定理,在f,g满足一定增长条件的前提下,证明了一类二阶两点微分方程系统边值问题:三个正解的存在性.其中:f,g:[0,1]×[0,∞)×R→[0,∞)连续.

By the uses of an improved Leggett-Willlams fixed-point theorem, and imposes some growth conditions on f,g. The existence of three positive solutions of the BVP for systems of second-oder two-point ODE with the form{u″（t）＋f（t,v（t）,v′（t））=0,0〈t〈1;v″（t）＋g（t,u（t）,u′（t））=0,0〈t〈1;u（0）=u（1）=v（0）=v（1）=0, is studied. Here, f,g： [0, 1]× [0,∞） × R→[0,∞） is continuous.