Abstract For an integro-differential equation of the convolution type defined on the half-line $$[0,\infty ) $$ with a power nonlinearity and an inhomogeneity in the linear part, we use the weight metrics method to prove a global theorem on the existence and uniqueness of a solution in the cone of nonnegative functions in the space $$C[0,\infty ) $$ . It is shown that the solution can be found by a successive approximation method of the Picard type; an estimate for the rate of convergence of the approximations is produced.

中文翻译：

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线性部分具有幂非线性和非齐次性的卷积型积分微分方程

摘要 对于定义在半线上的卷积型积分微分方程$$[0,\infty ) $$ 具有幂非线性和线性部分的不均匀性，我们使用权重度量方法证明全局定理关于空间 $$C[0,\infty ) $$ 中非负函数锥中解的存在性和唯一性。结果表明，可以通过Picard类型的逐次逼近方法找到该解；产生近似收敛速度的估计。