Application of the Leray–Schauder alternative to nonlinear singular operator equations

In this paper, we study the problem of existence of solution of nonlinear singular integral equations of the form {w(z)=Φ(z)+TGF(⋅,w(⋅),h(⋅))(z)h(z)=Φ′(z)+ΠGF(⋅,w(⋅),h(⋅))(z),z∈G⊂C.