Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University514910.18287/2541-7525-2017-23-2-26-31UnknownABOUT ONE NONLOCAL TASK FOR THE EQUATION OF THE FOURTH ORDER WITH THE DOMINATING MIXED DERIVATIVEKirichenkoS. V.morenov@ssau.ruSamara State University of Railway Transport2109201723226312109201721092017Copyright © 1970, Kirichenko S.V.1970<p>In the article the nonlocal task for the model equation from the dominating mixed derivative of the fourth order is considered. The unique solubility of an objective in which two of four conditions are nonlocal is proved and represent integrals both on a space variable, and on time variable. For the proof the new method based on equivalence of an objective and set of equations of the second order is offered.</p>псевдогиперболическое уравнение, нелокальная задача, интегральные условия, доминирующая производная.pseudo-hyperbolic equation, nonlocal task, integral conditions, dominating derivative.[[1] Utkina Е.А. Ob odnom uravnenii v chastnykh proizvodnykh chetvertogo poriadka [About one partial equation of the fourth order]. Differentsial’nye uravneniia [Differential equations], Minsk, 1999, 13 p. VINITI. 28.06.99 № 2059–В99 [in Russian].][[2] Zеgalov V.I., Mironov А.N. Differentsial’nye uravneniia so starshimi chastnymi proizvodnymi [Differential equations with the senior partial derivatives]. Kazan: Kazanskoe matem. o-vo, 2001, 226 p. [in Russian].][[3] Pulkina L.S. Zadachi s neklassicheskimi usloviiami dlia giperbolicheskikh uravnenii [Problems with nonclassical conditions for the hyperbolic equations]. Samara: Samarskii universitet, 2012, 196 p. [in Russian].][[4] Beylina N.V. Nelokal’naia zadacha s integral’nymi usloviiami dlia psevdogiperbolicheskogo uravneniia [Nonlocal task with integral conditions for the pseudo-hyperbolic equation]. Vestnik SamGU [Vestnik of Samara State University], 2008, no. 2, pp. 22–28 [in Russian].][[5] Kirichenko S.V. Zadacha s nelokal’nym integral’nym usloviem dlia psevdogiperbolicheskogo uravneniia chetvertogo poriadka [Task with a nonlocal integral condition for the pseudo-hyperbolic equation of the fourth order]. Vestnik SamGU [Vestnik of Samara State University], 2014, no. 3, pp. 42–51 [in Russian].][[6] Uldashev Т.К. Ob odnom smeshannom differentsial’nom uravnenii chetvertogo poriadka [About one mixed differential equation of the fourth order]. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta [Proceedings of the Institute of Mathematics and Informatics at Udmurt State University], 2016, Issue 1(47), pp. 119–127 [in Russian].]