m点边值共振问题的上下解和拓扑度

The upper and lower solutions of m-point boundary value problems at resonance and topological degree

研究拓扑度与二阶m点边值共振问题u″(t) =f(t,u(t) ,u′(t) ) , t∈ (0 ,1)u′(0 ) =0 , u(1) =∑m-1i=1aiu(ξi)的上下解之间的关系 .其中f:[0 ,1]×R2 R连续 ,ai 和 ξi∈ [0 ,∞ )为满足 ∑m-1i=1ai =1及 0 =ξ1<ξ2<… <ξm - 1<ξm=1的给定常数 .

The relation between the topological degree and strict upper and lower solutions is studied for second order m-point bound ary value problemu″(t)=f(t,u(t),u′(t)), t∈(0,1) u′(0)=0, u(1)=∑m-1i=1a iu(ξ i).Where f:×R 2R is continuous,a i and ξ i∈∞) are given constants such that ∑m-1i=1 a i=1 and 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1.