【摘要】 在不假定核函数非负的条件下,利用锥与半序方法及不动点指数理论,结合线性算子的谱半径,讨论了非线性Hammerstein型积分方程非零解的存在性。并将所得抽象结果具体应用于常微分方程两点边值问题,得到了上列积分方程存在非零解的新结论。更多还原

【Abstract】 In the case of not requiring the kernel function non-positive, the existence of nontrivial solutions for Hammerstein Integral Equations is proved by using the partial ordering and the fixed point index theory with the spectral radius of linear operators. The results are applied to ordinary differential equations with two-point values and new conclusions are obtained.更多还原