A solution of a nonlinear integral equation
Among various frequently used linear and nonlinear integral equations, which play important role in functional analysis, the authors consider the integral equation \[ \varphi(x,t)= f(x,t)+ \int^1_0 k(x,y) \gamma(y,\varphi(y, t))\,dy+ \int^t_0 F(t,\tau)\,\varphi(x,\tau)\,d\tau, \] where the notations are explained in the paper. Existence of the solution of the above Hammer\-stein-Volterra type equation of the second, is proved by employing the DeBlasi measure of weak non-compactness and the Schauder fixed point theorem. The paper is supported with relevant definitions and remarks. The authors give all known theorems in Section 2 as ready references. It is believed (reviewer's conjecture) that the integral equation, considered in this paper, may be studied as a distributional integral equation and, as a fractional equation.
nonlinear Hammerstein-Volterra integral equation
De Blasi measure of weak non-compactness
scientific article; zbMATH DE number 2137388