Nonlinear integro-differential equations with difference kernels

This paper is a summary of recent results obtained for nonlinear integro-differential equations of convolution type and singular integro-differential equations with Hilbert and Cauchy kernels. For nonnegative continuous solutions, we use the method of weight metrics (an analog, while for summable solutions on arbitrary sign, the “monotonicity” method (the Minty–Browder monotone operators) is applied.