We consider a class of nonlinear difference equations of the fourth order, which extends some equations in the literature. It is shown that the class of equations is solvable in closed form explaining theoretically, among other things, solvability of some previously considered very special cases. We also present some applications of the main theorem through two examples, which show that some results in the literature are not correct.

Based on the principles derived from Campbell?s theorem, this paper carries out an analysis of the possibilities of Campbell?s mean square value signal processing system. The mean square value mode is especially suitable for measurements performed in a mixed radiation field, because the quantities of electrical charge involved in the interactions of the two types of radiation are substantially different. The measuring detector element may be an adequate ionization chamber and/or semiconductor components for mixed n-? fields. An examination of the discrimination of gamma in relation to the neutron component in the signal of the detector output was carried out, calculated according to the theoretical model of radiation interaction with the detector. The advantage of the mean square value method was confirmed and it was concluded that the order of n-? discrimination in mean square value signal processing is greater than the one rendered by the classical measuring method.

Here we show that the main results in the papers by Yalcinkaya (2008), Yalcinkaya and Cinar (2010), and Yalcinkaya, Cinar, and Simsek (2008), as well as a conjecture from the last mentioned paper, follow from a slight modification of a result by G. Papaschinopoulos and C. J. Schinas. We also give some generalizations of these results.