Nonlinear Singular Integro-Differential Equations with an Arbitrary Parameter

The maximally monotone operator method in real weighted Lebesgue spaces is used to study three different classes of nonlinear singular integro-differential equations with an arbitrary positive parameter. Under sufficiently clear on the nonlinearity, we prove existence and uniqueness theorems for the solution covering in particular, the linear case as well. In contrast to the previous papers in which other classes of nonlinear singular integral and integro-differential equations were studied, our study is based on the inversion of the superposition operator generating the nonlinearities of the equations under consideration and the establishment of the coercitivity of the inverse operator, as well as a generalization of the well-known Schleiff inequality.