On the theory of an integral equation (Q1338884)

The main object of the study in the paper is the following integral equation (1) \(x(t) = f(t) - \mu \int^ \infty_ 0 K(\tau) \text{sign} [x(t - \tau)] d \tau\). Here it is assumed that \(\mu \geq 0\), \(f\) is a continuous function having only isolated zeros \(t_ k\) such that \(f'(t_ k) \neq 0\) for \(k=1,2, \dots\). Moreover, the kernel function \(K\) satisfies some assumptions expressed in terms of the possibility to be applied in the description of electrical circuits. The author considers many qualitative properties of the solution of the equation (1) which appear in the modern electrical and electronics industry and technology. For example, the oscillatory and periodicity character of solutions of (1) is studied in connection with the resistance, voltage and sensitivity of electrical circuits. In the reviewer's opinion the paper has rather purely applied character. It can be recommended to workers in electrical engineering.