Abstract: We address existence and multiplicity of positive solutions in boundary value problems of secondorder ordinary differential equations,u″(t)+λh1(t)f(u,v)=0,v″(t)+λh2(t)g(u,v)=0,u(0)=u(1)=v(0)=v(1)=0. With fixed point theorem and f(u,v) and g(u,v) satisfying a growth condition,we determine the scope of system parameter λ,which can ensure the system contains at least one or two positive solutions.

Key words: boundary value problems, positive solutions, multiple positive solutions, fixed point