非线性Hammerstein积分方程组的可解性

Solvability of Systems of Nonlinear Hammerstein Integral Equations

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.