摘要
利用Leggett-Williams不动点定理,并赋予f,g一定的增长条件,证明了二阶多点微分方程组边值问题u″+f(t,u,v)=0,v″+g(t,u,v)=0,0≤t≤1,u(0)=v(0)=0,u(1)-∑n-2i=1kiu(ξi)=0,v(1)-∑m-2i=1liv(ηi)=0,至少存在三对正解,其中f,g:[0,1]×[0,∞)×[0,∞)→[0,∞)是连续的.
We apply Leggett-Williams fixed point theorem to discuss multi-point boundary value problem of the second-order differential equation system
{u＂＋f（t,u,v）=0,0≤t≤1,
u＂＋g（t,u,v）=0,0≤t≤1,
u（0）=v（0）=0,u（1）-∑n-2i=1kiu（ξi）=0
v（0）=0,v（1）-∑m-2i=1liv（ηi）=0
where f,g：[0,1] × [0,∞） × [0,∞） → [0,∞） are continuous, growth conditions are imposed on f,g, which yield the existence of at least three positive solutions for the system.
出处
《数学的实践与认识》
CSCD
北大核心
2007年第5期134-139,共6页
Mathematics in Practice and Theory
