Integral Equations with Power Sum Kernel and Monotonic Nonlinearity

We use methods of the theory of monotone (in the Browder–Minty sense) operators to prove global theorems on the existence, uniqueness, and solution norm estimates for various classes of nonlinear integral equations with power sum kernel in the real Lebesgue spaces. Corollaries illustrating the obtained results are presented. Under additional assumptions, it is shown that solutions can be found by the method of successive approximations of the Picard type without restrictions on the values of the scalar parameter. These theorems cover the corresponding linear integral equations.