Hammerstein非线性积分方程组的非平凡解及应用

Nontrivial Solutions of Systems of Nonlinear Hammerstein Integral Equations and Applications

该文利用拓扑方法和锥理论研究下列Hammerstein非线性积分方程组在适当的条件下,证明了上述方程组非平解的存在性,并把所得结果应用于研究非线性二阶常微分方程组边值问题的非平凡解的存在性．

In this paper, by using topological methods and cone theory, the author studies the system of nonlinear Hammesrstein integral equations {u（x）=∫Gk（x,y）f（y,u（y）,v（y））dy,v（x）=∫Gk（x,y）g（y,u（y）,v（y））dyThe author proves the existence of nontrivial solutions of the above system under appropriate conditions. And the main results are applied to study the existence of nontrivial solutions of boundary value problems for systems of nonlinear second order ordinary differential equations.