The Existence of Multiple Positive Solutions in Boundary Value Problem of A Class of Second-order Ordinary Differential Systems

For the second-order nonlinear multi-point boundary value problems as follow:u″(t)+f(t,v(t))=0,0≤t≤1;v″(t)+g(t,u(t))=0,0≤t≤1;u′(0)=∑i=1 m-2 biu′(ξi),u(1)=∑i=1 k aiu(ξi)-∑i=k+1 m-2 aiu(ξi),v′(0)=∑i=1 m-2 diu′(ηi),v(1)=∑i=1 l civ(ηi)-∑i=l+1 m-2 civ(ηi),where f,g∈C(×[0,∞),[0,∞)),growth conditions are imposed on f,g which yield the existence of at least three solutions by a fixed point theorem.