二阶多点边值问题多个正解存在性  

The Existence of Multiple Positive Solutions for Second-order Multiple Points Boundary Value Problem Systems

作　　者：魏玉冬[1] 白随平[1] 姚立[1] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061

出　　处：《数学的实践与认识》2007年第5期134-139,共6页Mathematics in Practice and Theory

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.

关 键 词：Leggett—Williams不动点定理 锥 正解 增长条件 

分 类 号：O175.8[理学—数学]