Nonlinear convolution-type equations in Lebesgue spaces

Abstract

Methods of the theory of monotone operators are used to prove global theorems on the existence and uniqueness of solutions, as well as on estimates of their norms, for various classes of nonlinear integral convolution-type equations in the real Lebesgue spaces Lp(0, 1). These theorems involve nonlinear equations with potential-type kernels, including logarithmic potential-type kernels, as well as the corresponding linear integral equations within the framework of the space L2(0, 1). Corollaries illustrating the obtained results are presented.