Applications of transmutations of vekua – erd´elyi - lowndes type to differential equations

In the paper we study an important class of transmutations. Transmutation theory is a well-known field of differential equations, by its methods many remarkable results on differential equations were received. We consider an important class of transmutations - Vekua-Erdelyi-Lowndes operators. These transmutations, which were introduced and studied by above mentioned mathematicians, transmute differential operators of different nature with a spectral parameter to similar operators without a spectral parameter. In particular, by this method explicit connection formulas are obtained for solutions of perturbed and unperturbed differential equations. To illustrate our results some special differential equations are considered.