二阶微分方程组多点边值问题解的存在性

EXISTENCE OF POSITIVE SOLUTIONS FOR SECOND- ORDER MULTIPLE POINTS BOUNDARY VALUE PROBLEM

利用双锥上的不动点定理并赋予，和g-定的增长条件，证明了二阶微分方程组多点边值问题{u^n＋f（t,u,kv）=0,v^n＋g（t,u,v）=0,u（0）=0,u（1）=m-2∑i=1 aiu（ξi）,v（0）=o,v（1）=m-2∑i=1 biv（ηi）两组正解的存在性．其中0=ξ0＜ξ1＜…＜ξm-1=0,0=η0＜η1＜…ηm-2＜ηm-1=1,ai≥0,t∈（0,1）,且f，g：[0，1]×R^＋×R^＋→R是连续的．

For a second -order and m -point boundary value problem as follows：{u^n＋f（t,u,kv）=0,v^n＋g（t,u,v）=0,u（0）=0,u（1）=m-2∑i=1 aiu（ξi）,v（0）=o,v（1）=m-2∑i=1 biv（ηi）where 0 =ξ0〈ξ1〈…〈ξm-1=0,0=η0〈η1〈…ηm-2〈ηm-1=1,ai≥0,t∈（0,1）,且f,g：[0,1]×R^＋×R^＋→Ris continuous. Using fixed point theorem in a double cone and endowing certain growth conditions to f and g , we prove the existence of two positive solutions for above problem.