【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.更多还原

【Abstract】 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,v″+g(t,u,v)=0,0t1,u(0)=0,u(1)-∑n-2i=1kiu(ξi)=0,v(0)=0,v(1)-∑m-2i=1liv(ηi)=0,where f,g:\×[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.更多还原