摘要
利用拓扑方法和锥理论研究了下列非线性Hammerstein积分方程组 :u(x) =∫Gk(x ,y)f1(y ,u(y) ,v(y) )dyv(x) =∫Gk(x ,y)f2 (y ,u(y) ,v(y) )dy在适当的条件下 ,我们证明了上述方程组非平凡解的存在性 。
In this paper we study by using topological methods and cone theory the system of nonlinerar Hammesrstein integral equations: u(x)=∫ Gk(x,y)f 1(y,u(y),v(y))dy v(x)=∫ Gk(x,y)f 2(y,u(y),v(y))dy We shall prove the existence of nontivial solutions of the above problem under s ome appropriate conditions. And the main results are applied to the study of the existence of nontrivial solutions of boundary value problems for systems of non linear second order ordinary differential equations.
出处
《怀化学院学报》
2004年第5期1-8,共8页
Journal of Huaihua University
关键词
积分方程组
锥
不动点
非平凡解
system of integral equations
cone
fixed point
nontrivial solution