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We prove the existence of positive solutions to the boundary-value problem $$ displaylines{ u''+lambda a(t)f(u,u')=0 cr u(0)=0,quad u(1)=sum^{m-2}_{i=1} a_i u(xi_i) ,, }$$ where $a$ is a continuous function that may change sign on $[0,1]$, $f$ is a continuous function with $f(0,0)>0$, and $lambda$ is a samll positive constant. For finding solutions we use the Leray-Schauder fixed point theorem.